The Double Star Sequences and the General Second Zagreb Index

TL;DR

This paper introduces the double star sequence and its inverse, linking it to the general second Zagreb index, and provides generating functions and recurrence relations for these indices.

Contribution

It defines new graph sequences related to the Zagreb index and establishes their mathematical properties and relationships, advancing graph theory methods.

Findings

Double star sequence and its inverse are mathematically characterized.

The general second Zagreb index is expressed via the double star sequence.

Derived generating function and recurrence relation for Zagreb indices.

Abstract

For a simple graph we introduce notions of the double star sequence, the double star frequently sequence and prove that these sequences are inverses of each other. As a consequence, we express the general second Zagreb index in terms of the double star sequence. Also, we calculate the ordinary generating function and a linear recurrence relation for the sequence of the general second Zagreb indexes.