Two Sufficient Conditions for Pancyclic Graphs

Abstract

This paper gives two sufficient conditions for a $2$-connected graph to be pancyclic. The first one is that the degree sum of every pair of nonadjacent vertices should not be less than $\frac{n}{2}+\delta$. The second is that the degree sum of every triple of independent vertices should not be less than $n+\delta$, where $n$ is the number of vertices and $\delta$ is the minimum degree of the graph.