A Sufficient Condition for Graphic Sequences with Given Largest and Smallest Entries, Length, and Sum

TL;DR

This paper establishes a sufficient condition for a degree sequence to be graphic, based on its extremal entries, length, and sum, extending previous results in graph theory.

Contribution

It generalizes a known bound for graphic sequences by incorporating the largest and smallest degrees, length, and sum into a unified sufficient condition.

Findings

Provides a new sufficient condition for graphic sequences.

Generalizes the Zverovich and Zverovich bound.

Enhances understanding of degree sequence realizability.

Abstract

We give a sufficient condition for a degree sequence to be graphic based on its largest and smallest elements, length, and sum. This bound generalizes a result of Zverovich and Zverovich.