The Hyper-Zagreb Index of Some Complement Graphs

The First and Second Zagreb Index of Complement Graph and Its Applications of Molecular Graph

“…Proposition 3.7: [12] Let G1, G2 be two simple connected graphs with n1, n2 vertices and m1, m2 edges, respectively, then…”

“…For a graph G, the degree of a vertex u is the number of edges incident to u, denoted by δG(u). The complement of G, denoted by G , is a simple graph on the same set of vertices V (G) in which two vertices u and v are adjacent, i.e., connected by an edge uv, if and only if they are not adjacent in G. ) − m, the degree of a vertex u in G, is the number of edges incident to u, denoted by δ G (u) = n − 1 − δG(u), [5], [6]. Then, M. Khalifeh et al [3] and K. Kiruthika [7] computed the first and second Zagreb indices of Cartesian product G1 × G2, composition G1 • G2, disjunction G1 ∨ G2, symmetric difference G1 ⊕ G2, join G1 + G2, tensor product G1 ⊗ G2, and strong product G1 * G2 of two graphs.…”

Topological Indices of Some New Graph Operations and Their Possible Applications

“…Chemical graphs are models of molecules, in which atoms are represented by vertices and chemical bonds by edges of a graph. The basic idea of chemical graph theory is the physicochemical properties of molecules can be studied by using the information in the mathematico-chemical literature [1], [2], [3], [4]. Throughout this paper, we consider a simple finite connected graph G. We respectively denote by p and q the cardinality of its vertices set V (G) and E(G).…”

“…Moreover, we have studied the correlation coefficient between them to investigate the effectiveness of these indices in practical applications. We refer the interested reader to [12], [13], [2], [14], [15] for some recent results.…”

The F-index and coindex of V-Phenylenic Nanotubes and Nanotorus and their molecular complement graphs

“…Here, we present the F-index and F-coindex and their topological polynomials of V-Phenylenic Nanotube V P HX[m, n] and V-Phenylenic Nanotorus V P HY [m, n] which are useful for surveying structure of nanotubes and nanotorus. Any unexplained terminology is standard, typically as in [16][17][18][19][20][21].…”