Graph Theory and Discrete Applied Mathematics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 8550

Special Issue Editor


E-Mail Website
Guest Editor
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
Interests: mathematical modelling; graph theory; combinatorial optimization

Special Issue Information

Dear Colleagues,

Nowadays, discrete mathematics has a wide range of applications in various branches of science, such as physics, chemistry, informatics, and computer sciences. In this Special Issue, we aim to provide an opportunity for the exchange of research results and interactions between researchers working in the fields of algorithms and discrete applied mathematics. We invite you to submit your new research in the fields of graph theory, combinatorics, and combinatorial optimization. Both the theoretical and practical appliable aspects of results are welcome.

Dr. Baoyindureng Wu
Guest Editor

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. Axioms 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 2400 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

  • graph structures
  • extremal graph theory
  • parameters of graphs
  • applications of graph theory
  • algorithms on graphs
  • enumerations of substructures of graphs
  • combinatorial optimization

Published Papers (7 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

12 pages, 312 KiB  
Article
Spectrum of the Cozero-Divisor Graph Associated to Ring Zn
by Mohd Rashid, Amal S. Alali, Wasim Ahmed and Muzibur Rahman Mozumder
Axioms 2023, 12(10), 957; https://doi.org/10.3390/axioms12100957 - 11 Oct 2023
Viewed by 834
Abstract
Let R be a commutative ring with identity 10 and let Z(R) be the set of all non-unit and non-zero elements of ring R. Γ(R) denotes the cozero-divisor graph of R and [...] Read more.
Let R be a commutative ring with identity 10 and let Z(R) be the set of all non-unit and non-zero elements of ring R. Γ(R) denotes the cozero-divisor graph of R and is an undirected graph with vertex set Z(R), wzR, and zwR if and only if two distinct vertices w and z are adjacent, where qR is the ideal generated by the element q in R. In this article, we investigate the signless Laplacian eigenvalues of the graphs Γ(Zn). We also show that the cozero-divisor graph Γ(Zp1p2) is a signless Laplacian integral. Full article
(This article belongs to the Special Issue Graph Theory and Discrete Applied Mathematics)
Show Figures

Figure 1

20 pages, 773 KiB  
Article
On the Normalized Laplacian Spectrum of the Linear Pentagonal Derivation Chain and Its Application
by Yuqing Zhang and Xiaoling Ma
Axioms 2023, 12(10), 945; https://doi.org/10.3390/axioms12100945 - 1 Oct 2023
Cited by 1 | Viewed by 790
Abstract
A novel distance function named resistance distance was introduced on the basis of electrical network theory. The resistance distance between any two vertices u and v in graph G is defined to be the effective resistance between them when unit resistors are placed [...] Read more.
A novel distance function named resistance distance was introduced on the basis of electrical network theory. The resistance distance between any two vertices u and v in graph G is defined to be the effective resistance between them when unit resistors are placed on every edge of G. The degree-Kirchhoff index of G is the sum of the product of resistance distances and degrees between all pairs of vertices of G. In this article, according to the decomposition theorem for the normalized Laplacian polynomial of the linear pentagonal derivation chain QPn, the normalize Laplacian spectrum of QPn is determined. Combining with the relationship between the roots and the coefficients of the characteristic polynomials, the explicit closed-form formulas for degree-Kirchhoff index and the number of spanning trees of QPn can be obtained, respectively. Moreover, we also obtain the Gutman index of QPn and we discovery that the degree-Kirchhoff index of QPn is almost half of its Gutman index. Full article
(This article belongs to the Special Issue Graph Theory and Discrete Applied Mathematics)
Show Figures

Figure 1

13 pages, 848 KiB  
Article
The Difference of Zagreb Indices of Halin Graphs
by Lina Zheng, Yiqiao Wang and Weifan Wang
Axioms 2023, 12(5), 450; https://doi.org/10.3390/axioms12050450 - 2 May 2023
Viewed by 870
Abstract
The difference of Zagreb indices of a graph G is defined as [...] Read more.
The difference of Zagreb indices of a graph G is defined as ΔM(G)=uV(G)(d(u))2uvE(G)d(u)d(v), where d(x) denotes the degree of a vertex x in G. A Halin graph G is a graph that results from a plane tree T without vertices of degree two and with at least one vertex of degree at least three such that all leaves are joined through a cycle C in the embedded order. In this paper, we establish both lower and upper bounds on the difference of Zagreb indices for general Halin graphs and some special Halin graphs with fewer inner vertices. Furthermore, extremal graphs attaining related bounds are found. Full article
(This article belongs to the Special Issue Graph Theory and Discrete Applied Mathematics)
Show Figures

Figure 1

13 pages, 345 KiB  
Article
Graphs with Strong Proper Connection Numbers and Large Cliques
by Yingbin Ma, Xiaoxue Zhang and Yanfeng Xue
Axioms 2023, 12(4), 353; https://doi.org/10.3390/axioms12040353 - 3 Apr 2023
Viewed by 1012
Abstract
In this paper, we mainly investigate graphs with a small (strong) proper connection number and a large clique number. First, we discuss the (strong) proper connection number of a graph G of order n and ω(G)=ni [...] Read more.
In this paper, we mainly investigate graphs with a small (strong) proper connection number and a large clique number. First, we discuss the (strong) proper connection number of a graph G of order n and ω(G)=ni for 1i3. Next, we investigate the rainbow connection number of a graph G of order n, diam(G)3 and ω(G)=ni for 2i3. Full article
(This article belongs to the Special Issue Graph Theory and Discrete Applied Mathematics)
Show Figures

Figure 1

8 pages, 444 KiB  
Article
On Several Parameters of Super Line Graph L2(G)
by Jiawei Meng, Baoyindureng Wu and Hongliang Ma
Axioms 2023, 12(3), 276; https://doi.org/10.3390/axioms12030276 - 6 Mar 2023
Viewed by 1299
Abstract
The super line graph of index r, denoted by Lr(G), is defined for any graph G with at least r edges. Its vertices are the sets of r edges of G, and two such sets are [...] Read more.
The super line graph of index r, denoted by Lr(G), is defined for any graph G with at least r edges. Its vertices are the sets of r edges of G, and two such sets are adjacent if an edge of one is adjacent to an edge of the other. In this paper, we give an explicit characterization for all graphs G with L2(G) being a complete graph. We present lower bounds for the clique number and chromatic number of L2(G) for several classes of graphs. In addition, bounds for the domination number of L2(G) are established in terms of the domination number of the line graph L(G) of a graph. A number of related problems on L2(G) are proposed for a further study. Full article
(This article belongs to the Special Issue Graph Theory and Discrete Applied Mathematics)
Show Figures

Figure 1

13 pages, 384 KiB  
Article
Extremal Graphs for Sombor Index with Given Parameters
by Wanping Zhang, Jixiang Meng and Na Wang
Axioms 2023, 12(2), 203; https://doi.org/10.3390/axioms12020203 - 15 Feb 2023
Cited by 2 | Viewed by 1261
Abstract
In this paper, we present the upper and lower bounds on Sombor index SO(G) among all connected graphs (respectively, connected bipartite graphs). We give some sharp lower and upper bounds on SO(G) among connected graphs [...] Read more.
In this paper, we present the upper and lower bounds on Sombor index SO(G) among all connected graphs (respectively, connected bipartite graphs). We give some sharp lower and upper bounds on SO(G) among connected graphs in terms of some parameters, including chromatic, girth and matching number. Meanwhile, we characterize the extremal graphs attaining those bounds. In addition, we give upper bounds on SO(G) among connected bipartite graphs with given matching number and/or connectivity and determine the corresponding extremal connected bipartite graphs. Full article
(This article belongs to the Special Issue Graph Theory and Discrete Applied Mathematics)
Show Figures

Figure 1

8 pages, 392 KiB  
Article
The Decomposability of Toroidal Graphs without Adjacent Triangles or Short Cycles
by Huajing Lu and Fengwei Li
Axioms 2023, 12(2), 173; https://doi.org/10.3390/axioms12020173 - 8 Feb 2023
Cited by 2 | Viewed by 1044
Abstract
A graph G has a (d,h)-decomposition if there is a pair (D,F) such that F is a subgraph of G and D is an acyclic orientation of GE(F), [...] Read more.
A graph G has a (d,h)-decomposition if there is a pair (D,F) such that F is a subgraph of G and D is an acyclic orientation of GE(F), where the maximum degree of F is no more than h and the maximum out-degree of D is no more than d. This paper proves that toroidal graphs having no adjacent triangles are (3,1)-decomposable, and for {i,j}{3,4,6}, toroidal graphs without i- and j-cycles are (2,1)-decomposable. As consequences of these results, toroidal graphs without adjacent triangles are 1-defective DP-4-colorable, and toroidal graphs without i- and j-cycles are 1-defective DP-3-colorable for {i,j}{3,4,6}. Full article
(This article belongs to the Special Issue Graph Theory and Discrete Applied Mathematics)
Show Figures

Figure 1

Back to TopTop