Spectral Conditions for the Bipancyclic Bipartite Graphs

TL;DR

This paper establishes spectral criteria that determine when bipartite graphs are bipancyclic, meaning they contain cycles of all even lengths from 4 up to the number of vertices.

Contribution

It introduces new spectral conditions that guarantee bipancyclicity in bipartite graphs, advancing understanding of spectral graph theory.

Findings

Spectral conditions for bipancyclicity derived

Conditions applicable to balanced bipartite graphs

Enhanced criteria for cycle existence in bipartite graphs

Abstract

Let $G = (X, Y; E)$ be a bipartite graph with two vertex partition subsets $X$ and $Y$. $G$ is said to be balanced if $|X| = |Y|$. $G$ is said to be bipancyclic if it contains cycles of every even length from $4$ to $|V(G)|$. In this note, we present spectral conditions for the bipancyclic bipartite graphs.