Some Sufficient Conditions on Pancyclic 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.

Wiener index and Harary index on pancyclic graphs

“…In this paper, we consider the problem of deciding whether a given graph is pancyclic. Yu et al [14] established some 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. Motivated by these results, we present some sufficient conditions for a graph to be pancyclic in terms of the Wiener index, the Harary index, the distance spectral radius and the Harary spectral radius of a graph, respectively.…”