The Zagreb coindices of graph operations

Abstract

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.

Reformulated First Zagreb Index of Some Graph Operations

“…In [12], Khalifeh et al, derived some exact expressions for computing first and second Zagreb indices of some graph operations. Ashrafi et al [13] derived explicit expressions for Zagreb coindices of different graph operations. Das et al [14] derived some upper bounds for multiplicative Zagreb indices of different graph operations.…”

GA2 index of some graph operations

“…In [17], Klavžar, Rajapakse and Gutman computed the Szeged index of the Cartesian product graphs. The recent authors, [1,2,9,11,12,13,14,15,16,18,24], computed some exact formulas for the hyper-Wiener, vertex PI, edge PI, the first Zagreb, the second Zagreb, the edge Wiener and the edge Szeged indices of some graph operations. The aim of this section is to continue this program for computing the GA 2 index of these graph operations.…”

A short note on hyper Zagreb index

“…In 2010, Ashrafi, Došlić and Hamzeha introduced the concept of sum of nonadjacent vertex degree pairs of the graph G, known as first and second Zagreb coindices [2] and are defined as…”