Abstract
The sigma coindex is defined as the sum of the squares of the differences between the degrees of all nonadjacent vertex pairs. In this paper, we propose some mathematical properties of the sigma coindex. Later, we present precise results for the sigma coindices of various graph operations such as tensor product, Cartesian product, lexicographic product, disjunction, strong product, union, join, and corona product.
Highlights
Let G be a simple graph with a vertex set V(G) and edge set
Chemical graph theory is the field of study of mathematical chemistry in relation to chemical graphs. e basic idea here is to reveal the properties of molecules using the information corresponding to chemical graphics
Topological indices are constant numbers that reveal the structure of the graph. ese constant numbers are used in the modeling of molecules in chemistry and biology
Summary
E(G), where |V(G)| nG and |E(G)| mG. e degree of a vertex g in G, denoted by degG(g), is defined as the number of incident edges to it. e complement of a G graph, denoted by G, is the graph with the same vertex set. Many topology indices have been defined and used as a tool in QSAR/QSPR studies. E hyper-Zagreb coindex was introduced by Veylaki et al [7], as are defined as follows:. After that Jahanbani and Ediz [9] presented the properties of this index under various graph products. With this motivation, we define the sigma coindex and the total sigma index as, respectively, σ(G) dG g1 − dG g22,. We will calculate the sigma coindex of two graphs under some graph products as corona, join, union, lexicographic product, disjunction, tensor product, Cartesian product, and strong product
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