f-polynomial on some graph operations

Given any function f:Z+→R+ , let us define the f-index If(G)=∑u∈V(G)f(du) and the f-polynomial Pf(G,x)=∑u∈V(G)x1/f(du)−1, for x>0 . In addition, we define Pf(G,0)=limx→0+Pf(G,x) . We use the f-polynomial of a large family of topological indices in order to study mathematical relations of the inverse degree, the generalized first Zagreb, and the sum lordeg indices, among others. In this paper, using this f-polynomial, we obtain several properties of these indices of some classical graph operations that include corona product and join, line, and Mycielskian, among others.

inverse degree index; generalized first zagreb index; sum lordeg index; corona product; join of graphs; line graph; mycielskian graph; polynomials in graphs

f-polynomial on some graph operations Articles