Two Sufficient Conditions for Pancyclic Graphs

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.