Some Sufficient Conditions on Pancyclic Graphs

TL;DR

This paper presents new sufficient conditions based on edge count and spectral properties that guarantee a graph is pancyclic, meaning it contains cycles of all lengths from three to the number of vertices.

Contribution

It introduces novel spectral and edge-based criteria that ensure pancyclicity, expanding the theoretical understanding of cycle structures in graphs.

Findings

Derived conditions involving spectral radius for pancyclicity.

Established bounds on edge number for pancyclic graphs.

Linked spectral properties to cycle existence in graphs.

Abstract

A pancyclic graph is a graph that contains cycles of all possible lengths from three up to the number of vertices in the graph. In this paper, we establish some new sufficient conditions for a graph to be pancyclic in terms of the edge number, the spectral radius and the signless Laplacian spectral radius of the graph.