The star sequence and the general first Zagreb index

Leonid Bedratyuk, Oleg Savenko

Published 2017-06-02Version 1

For a simple graph, we introduce a notion of the star sequence and prove that the star sequence and the frequently sequences of a graph are inverses of each other from a combinatorial point of view. As a consequence, we express the general first Zagreb index in terms of the star sequence. Also, we calculate the ordinary generating function and find a linear recurrence relation for the sequence of the general first Zagreb indexes.