Special Issue "Graph Labelings and Their Applications"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics and Symmetry/Asymmetry".

Deadline for manuscript submissions: closed (15 May 2022) | Viewed by 13869

Special Issue Editors

Dr. Andrea Semaničová-Feňovčíková
E-Mail Website
Guest Editor
Department of Applied Mathematics and Informatics, Faculty of Mechanical Engineering, Technical University in Košice, Košice, Slovakia
Interests: graph labelings; metric dimension of graphs
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Martin Bača
E-Mail Website
Guest Editor
Department of Applied Mathematics and Informatics, Faculty of Mechanical Engineering, Technical University in Košice, Košice, Slovakia
Interests: graph labelings; metric dimension of graphs
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Among the huge diversity of concepts that appear while studying graph theory, one that has gained a lot of popularity is the concept of labelings of graphs. Graph labelings provide useful mathematical models for a wide range of applications in high technologies (data security, cryptography (secret sharing schemes), astronomy, various coding theory problems, communication networks, etc.). A labeling or a valuation of a graph is any mapping that sends a certain set of graph elements to a certain set of numbers subject to certain conditions.

Please note that all submitted papers must be within the general scope of the Symmetry journal.

Prof. Dr. Andrea Semaničová-Feňovčíková
Prof. Dr. Martin Bača
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Graceful labelings and their variations
  • Magic-type labelings
  • Antimagic-type labelings
  • Irregular-type labelings
  • Sum labelings and their variations
  • Prime and vertex prime labelings
  • Binary labelings
  • Average labelings
  • Labelings and their induced colorings
  • Applications of graph labelings

Published Papers (11 papers)

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Research

Article
Antimagic Labeling for Product of Regular Graphs
Symmetry 2022, 14(6), 1235; https://doi.org/10.3390/sym14061235 - 14 Jun 2022
Viewed by 1010
Abstract
An antimagic labeling of a graph G=(V,E) is a bijection from the set of edges of G to 1,2,,E(G) and such that any two vertices of G have [...] Read more.
An antimagic labeling of a graph G=(V,E) is a bijection from the set of edges of G to 1,2,,E(G) and such that any two vertices of G have distinct vertex sums where the vertex sum of a vertex v in V(G) is nothing but the sum of all the incident edge labeling of G. In this paper, we discussed the antimagicness of rooted product and corona product of graphs. We proved that if we let G be a connected t-regular graph and H be a connected k-regular graph, then the rooted product of graph G and H admits antimagic labeling if tk. Moreover, we proved that if we let G be a connected t-regular graph and H be a connected k-regular graph, then the corona product of graph G and H admits antimagic labeling for all t,k2. Full article
(This article belongs to the Special Issue Graph Labelings and Their Applications)
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Article
Open Support of Hypergraphs under Addition
Symmetry 2022, 14(4), 669; https://doi.org/10.3390/sym14040669 - 24 Mar 2022
Viewed by 744
Abstract
For a vertex v in a graph G, the open support of v under addition is the sum of degrees of all its neighbors. The open support of G under addition is the sum of open supports of all its vertices. The [...] Read more.
For a vertex v in a graph G, the open support of v under addition is the sum of degrees of all its neighbors. The open support of G under addition is the sum of open supports of all its vertices. The results for open support of graphs are deeply dependent on the structure property of the graph considered, such as its symmetry. In this paper, we generalize the concept of open support to hypergraphs. We give some examples and prove a general formula for open support of hypergraphs by using the adjacency and incidence matrices method. Full article
(This article belongs to the Special Issue Graph Labelings and Their Applications)
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Article
D-Magic Oriented Graphs
Symmetry 2021, 13(12), 2261; https://doi.org/10.3390/sym13122261 - 27 Nov 2021
Cited by 1 | Viewed by 837
Abstract
In this paper, we define D-magic labelings for oriented graphs where D is a distance set. In particular, we label the vertices of the graph with distinct integers {1,2,,|V(G)|} [...] Read more.
In this paper, we define D-magic labelings for oriented graphs where D is a distance set. In particular, we label the vertices of the graph with distinct integers {1,2,,|V(G)|} in such a way that the sum of all the vertex labels that are a distance in D away from a given vertex is the same across all vertices. We give some results related to the magic constant, construct a few infinite families of D-magic graphs, and examine trees, cycles, and multipartite graphs. This definition grew out of the definition of D-magic (undirected) graphs. This paper explores some of the symmetries we see between the undirected and directed version of D-magic labelings. Full article
(This article belongs to the Special Issue Graph Labelings and Their Applications)
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Article
Another Antimagic Conjecture
Symmetry 2021, 13(11), 2071; https://doi.org/10.3390/sym13112071 - 02 Nov 2021
Cited by 3 | Viewed by 1019
Abstract
An antimagic labeling of a graph G is a bijection f:E(G){1,,|E(G)|} such that the weights [...] Read more.
An antimagic labeling of a graph G is a bijection f:E(G){1,,|E(G)|} such that the weights w(x)=yxf(y) distinguish all vertices. A well-known conjecture of Hartsfield and Ringel (1990) is that every connected graph other than K2 admits an antimagic labeling. For a set of distances D, a D-antimagic labeling of a graph G is a bijection f:V(G){1,,|V(G)|} such that the weightω(x)=yND(x)f(y) is distinct for each vertex x, where ND(x)={yV(G)|d(x,y)D} is the D-neigbourhood set of a vertex x. If ND(x)=r, for every vertex x in G, a graph G is said to be (D,r)-regular. In this paper, we conjecture that a graph admits a D-antimagic labeling if and only if it does not contain two vertices having the same D-neighborhood set. We also provide evidence that the conjecture is true. We present computational results that, for D={1}, all graphs of order up to 8 concur with the conjecture. We prove that the set of (D,r)-regular D-antimagic graphs is closed under union. We provide examples of disjoint union of symmetric (D,r)-regular that are D-antimagic and examples of disjoint union of non-symmetric non-(D,r)-regular graphs that are D-antimagic. Furthermore, lastly, we show that it is possible to obtain a D-antimagic graph from a previously known distance antimagic graph. Full article
(This article belongs to the Special Issue Graph Labelings and Their Applications)
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Article
On Forbidden Subgraphs of (K2, H)-Sim-(Super)Magic Graphs
Symmetry 2021, 13(8), 1346; https://doi.org/10.3390/sym13081346 - 26 Jul 2021
Viewed by 1177
Abstract
A graph G admits an H-covering if every edge of G belongs to a subgraph isomorphic to a given graph H. G is said to be H-magic if there exists a bijection [...] Read more.
A graph G admits an H-covering if every edge of G belongs to a subgraph isomorphic to a given graph H. G is said to be H-magic if there exists a bijection f:V(G)E(G){1,2,,|V(G)|+|E(G)|} such that wf(H)=vV(H)f(v)+eE(H)f(e) is a constant, for every subgraph H isomorphic to H. In particular, G is said to be H-supermagic if f(V(G))={1,2,,|V(G)|}. When H is isomorphic to a complete graph K2, an H-(super)magic labeling is an edge-(super)magic labeling. Suppose that G admits an F-covering and H-covering for two given graphs F and H. We define G to be (F,H)-sim-(super)magic if there exists a bijection f that is simultaneously F-(super)magic and H-(super)magic. In this paper, we consider (K2,H)-sim-(super)magic where H is isomorphic to three classes of graphs with varied symmetry: a cycle which is symmetric (both vertex-transitive and edge-transitive), a star which is edge-transitive but not vertex-transitive, and a path which is neither vertex-transitive nor edge-transitive. We discover forbidden subgraphs for the existence of (K2,H)-sim-(super)magic graphs and classify classes of (K2,H)-sim-(super)magic graphs. We also derive sufficient conditions for edge-(super)magic graphs to be (K2,H)-sim-(super)magic and utilize such conditions to characterize some (K2,H)-sim-(super)magic graphs. Full article
(This article belongs to the Special Issue Graph Labelings and Their Applications)
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Article
On SD-Prime Labelings of Some One Point Unions of Gears
Symmetry 2021, 13(5), 849; https://doi.org/10.3390/sym13050849 - 11 May 2021
Cited by 1 | Viewed by 960
Abstract
Let G=(V(G),E(G)) be a simple, finite and undirected graph of order n. Given a bijection f:V(G){1,,n}, [...] Read more.
Let G=(V(G),E(G)) be a simple, finite and undirected graph of order n. Given a bijection f:V(G){1,,n}, and every edge uv in E(G), let S=f(u)+f(v) and D=|f(u)f(v)|. The labeling f induces an edge labeling f:E(G){0,1} such that for an edge uv in E(G), f(uv)=1 if gcd(S,D)=1, and f(uv)=0 otherwise. Such a labeling is called an SD-prime labeling if f(uv)=1 for all uvE(G). We provide SD-prime labelings for some one point unions of gear graphs. Full article
(This article belongs to the Special Issue Graph Labelings and Their Applications)
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Article
The Irregularity and Modular Irregularity Strength of Fan Graphs
Symmetry 2021, 13(4), 605; https://doi.org/10.3390/sym13040605 - 06 Apr 2021
Cited by 8 | Viewed by 1330
Abstract
For a simple graph G with no isolated edges and at most, one isolated vertex, a labeling φ:E(G){1,2,,k} of positive integers to the edges of G is called [...] Read more.
For a simple graph G with no isolated edges and at most, one isolated vertex, a labeling φ:E(G){1,2,,k} of positive integers to the edges of G is called irregular if the weights of the vertices, defined as wtφ(v)=uN(v)φ(uv), are all different. The irregularity strength of a graph G is known as the maximal integer k, minimized over all irregular labelings, and is set to ∞ if no such labeling exists. In this paper, we determine the exact value of the irregularity strength and the modular irregularity strength of fan graphs. Full article
(This article belongs to the Special Issue Graph Labelings and Their Applications)
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Article
Graphs with Minimal Strength
Symmetry 2021, 13(3), 513; https://doi.org/10.3390/sym13030513 - 21 Mar 2021
Cited by 3 | Viewed by 1056
Abstract
For any graph G of order p, a bijection f:V(G){1,2,,p} is called a numbering of G. The strength strf(G) of [...] Read more.
For any graph G of order p, a bijection f:V(G){1,2,,p} is called a numbering of G. The strength strf(G) of a numbering f of G is defined by strf(G)=max{f(u)+f(v)|uvE(G)}, and the strength str(G) of a graph G is str(G)=min{strf(G)|f is a numbering of G}. In this paper, many open problems are solved, and the strengths of new families of graphs are determined. Full article
(This article belongs to the Special Issue Graph Labelings and Their Applications)
Article
H-Irregularity Strengths of Plane Graphs
Symmetry 2021, 13(2), 229; https://doi.org/10.3390/sym13020229 - 30 Jan 2021
Cited by 1 | Viewed by 1010
Abstract
Graph labeling is the mapping of elements of a graph (which can be vertices, edges, faces or a combination) to a set of numbers. The mapping usually produces partial sums (weights) of the labeled elements of the graph, and they often have an [...] Read more.
Graph labeling is the mapping of elements of a graph (which can be vertices, edges, faces or a combination) to a set of numbers. The mapping usually produces partial sums (weights) of the labeled elements of the graph, and they often have an asymmetrical distribution. In this paper, we study vertex–face and edge–face labelings of two-connected plane graphs. We introduce two new graph characteristics, namely the vertex–face H-irregularity strength and edge–face H-irregularity strength of plane graphs. Estimations of these characteristics are obtained, and exact values for two families of graphs are determined. Full article
(This article belongs to the Special Issue Graph Labelings and Their Applications)
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Article
Modular Edge-Gracefulness of Graphs without Stars
Symmetry 2020, 12(12), 2013; https://doi.org/10.3390/sym12122013 - 06 Dec 2020
Viewed by 804
Abstract
We investigate the modular edge-gracefulness k(G) of a graph, i.e., the least integer k such that taking a cyclic group Zk of order k, there exists a function f:E(G)Zk so [...] Read more.
We investigate the modular edge-gracefulness k(G) of a graph, i.e., the least integer k such that taking a cyclic group Zk of order k, there exists a function f:E(G)Zk so that the sums of edge labels incident with every vertex are distinct. So far the best upper bound on k(G) for a general graph G is 2n, where n is the order of G. In this note we prove that if G is a graph of order n without star as a component then k(G)=n for n¬2(mod4) and k(G)=n+1 otherwise. Moreover we show that for such G for every integer tk(G) there exists a Zt-irregular labeling. Full article
(This article belongs to the Special Issue Graph Labelings and Their Applications)
Article
Local Super Antimagic Total Labeling for Vertex Coloring of Graphs
Symmetry 2020, 12(11), 1843; https://doi.org/10.3390/sym12111843 - 07 Nov 2020
Cited by 4 | Viewed by 1446
Abstract
Let G=(V,E) be a graph with vertex set V and edge set E. A local antimagic total vertex coloring f of a graph G with vertex-set V and edge-set E is an injective map from [...] Read more.
Let G=(V,E) be a graph with vertex set V and edge set E. A local antimagic total vertex coloring f of a graph G with vertex-set V and edge-set E is an injective map from VE to {1,2,,|V|+|E|} such that if for each uvE(G) then w(u)w(v), where w(u)=uvE(G)f(uv)+f(u). If the range set f satisfies f(V)={1,2,,|V|}, then the labeling is said to be local super antimagic total labeling. This labeling generates a proper vertex coloring of the graph G with the color w(v) assigning the vertex v. The local super antimagic total chromatic number of graph G, χlsat(G) is defined as the least number of colors that are used for all colorings generated by the local super antimagic total labeling of G. In this paper we investigate the existence of the local super antimagic total chromatic number for some particular classes of graphs such as a tree, path, cycle, helm, wheel, gear, sun, and regular graphs as well as an amalgamation of stars and an amalgamation of wheels. Full article
(This article belongs to the Special Issue Graph Labelings and Their Applications)
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