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...
A domination coloring of a graph G is a proper vertex coloring of G, such that each vertex of G dominates at least one color class (possibly its own class), and each color class is dominated by at least one vertex. The minimum number of colors among...
A distance antimagic graph is a graph G admitting a bijection f:V(G)→{1,2,…,|V(G)|} such that for two distinct vertices x and y, ω(x)≠ω(y), where ω(x)=∑y∈N(x)f(y), for N(x) the open neighborhood of x. It was...
The clustering coefficient of a vertex v, of degree at least 2, in a graph Γ is obtained using the formula C(v)=2t(v)deg(v)(deg(v)−1), where t(v) denotes the number of triangles of the graph containing v as a vertex, and the clustering co...
The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. The additively weighted Harary index H A ( G ) is a modification of the Harary index in which the contributions of vert...
The graph centroids defined through a topological property of a graph called g-convexity found its application in various fields. They have classified under the “facility location” problem. However, the g-centroid location for an arbitrar...
Given any function f : Z + → R + , let us define the f-index I f ( G ) = ∑ u ∈ V ( G ) f ( d u ) and the f-polynomial P f ( G , x ) = ∑ u ∈ V ( G ) x 1 / f ( d u ) − 1 ,...
Let G be a connected, simple, and finite graph. For an ordered set W={w1,w2,…,wk}⊆V(G) and a vertex v of G, the representation of v with respect to W is the k-vector r(v|W)=(dG(v,w1),…,dG(v,wk)). The set W is called a resolving set...
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused the global pandemic, coronavirus disease-2019 (COVID-19) which has resulted in 60.4 million infections and 1.42 million deaths worldwide. Mathematical models as an integral part...
The independent number of a graph G is the cardinality of the maximum independent set of G, denoted by α ( G ) . The independent dominating number is the cardinality of the smallest independent set that dominates all vertices of G. In th...
In 2013 the concept of [j,k]-dominating sets in graphs have been introduced as an extension of [1,k]-dominating sets. Regarding studying [j,k]-dominating sets, the research is also interesting if the additional independence requirement is assumed, be...
It is well-known that the different products of graphs are some of the more symmetric classes of graphs. Since we are interested in hyperbolicity, it is interesting to study this property in products of graphs. Some previous works characterize the hy...
In 2008, Hedetniemi et al. introduced (1,k)-domination in graphs. The research on this concept was extended to the problem of existence of independent (1,k)-dominating sets, which is an NP-complete problem. In this paper, we consider independent (1,1...
The correlations between the physico-chemical properties of a chemical structure and its molecular structure-properties are used in quantitative structure-activity and property relationship studies (QSAR/QSPR) by using graph-theoretical analysis and...
A dominating set is a classic concept that is widely used in road safety, disaster rescue operations, and chemical graphs. In this paper, we introduce a variation of the dominating set: the proper 3-dominating set. For a proper 3-dominating set D of...
Some years ago, the harmonic polynomial was introduced to study the harmonic topological index. Here, using this polynomial, we obtain several properties of the harmonic index of many classical symmetric operations of graphs: Cartesian product, coron...
Tree-width and path-width are well-known graph parameters. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width and path-w...
The study of networks and graphs carried out by topological measures performs a vital role in securing their hidden topologies. This strategy has been extremely used in biomedicine, cheminformatics and bioinformatics, where computations dependent on...
A topological index is a number that is connected to a chemical composition in order to correlate a substance’s chemical makeup with different physical characteristics, chemical reactivity, or biological activity. It is common to model drugs an...
Let G be a graph with vertex set V(G) and f:V(G)→{∅,{1},{2},{1,2}} be a function. We say that f is an outer-independent 2-rainbow dominating function on G if the following two conditions hold: (i)V∅={x∈V(G):f(x)=∅} is an i...