Let G be a simple graph with vertex set {v1, v2, … , vn}. The common neighborhood graph of G, denoted by con(G), is a graph with vertex set {v1, v2, … , vn}, in which two vertices are adjacent if and only if they have at least one common neighbor in the graph G. In this paper, we compute the common neighborhood of some composite graphs. In continue, we investigate the relation between hamiltoni...

The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiene...

Let G be a simple connected graph. The first and second Zagreb indices have been introduced as  vV(G) (v)2 M1(G) degG and M2(G)  uvE(G)degG(u)degG(v) , respectively, where degG v(degG u) is the degree of vertex v (u) . In this paper, we define a new distance-based named HyperZagreb as e uv E(G) . (v))2 HM(G)     (degG(u)  degG In this paper, the HyperZagreb index of the Cartesian p...

In this paper, some applications of our earlier results in working with chemical graphs are presented.

In this paper, the Hyper - Zagreb index of the Cartesian product, composition and corona product of graphs are computed. These corrects some errors in G. H. Shirdel et al.[11].

We prove a general result on graph factors modulo k. A special case says that, for each natural number k, every (12k − 7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k.

A tight k-uniform `-cycle, denoted by TC ` , is a k-uniform hypergraph whose vertex set is v0, · · · , v`−1, and the edges are all the k-tuples {vi, vi+1, · · · , vi+k−1}, with subscripts modulo k. Motivated by a classic result in graph theory that every n-vertex cycle-free graph has at most n− 1 edges, Sós and, independently, Verstraëte asked whether for every integer k, a k-uniform n-vertex h...

A graph is pseudo 2–factor isomorphic if the numbers of circuits of length congruent to zero modulo four in each of its 2–factors, have the same parity. We prove that there exist no pseudo 2–factor isomorphic

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...