a b s t r a c tRecently introduced Zagreb coindices are a generalization of classical Zagreb indices of chemical graph theory. We explore here their basic mathematical properties and present explicit formulae for these new graph invariants under several graph operations.
Let G be a finite group. The power graph P(G) and its main supergraph S(G) are two simple graphs with the same vertex set G. Two elements x, y ∈ G are adjacent in the power graph if and only if one is a power of the other. They are joined in S(G) if and only if o(x)|o(y) or o(y)|o(x). The aim of this paper is to compute the characteristic polynomial of these graph for certain finite groups. As a consequence, the spectrum and Laplacian spectrum of these graphs for dihedral, semi-dihedral, cyclic and dicyclic groups were computed.
The power graph P(G) is a graph with group elements as a vertex set and two elements are adjacent if one is a power of the other. The order supergraph S(G) of the power graph P(G) is a graph with vertex set G in which two elements x, y ∈ G are joined if o(x)|o(y) or o(y)|o(x). The purpose of this paper is to study certain properties of this new graph together with the relationship between P(G) and S(G) .
The degree distance, Zagreb coindices and reverse degree distance of a connected graph have been studied in mathematical chemistry. In this paper some new extremal values of these topological invariants over some special classes of graphs are determined.
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