A new result about panconnectivity on graphs (Q1179497)

The principal result of this paper is the following. Let \(G\) be a graph with \(n\geq 9\) vertices such that the sum of the degrees of any two independent vertices of \(G\) is at least \(n-1\). Then \(G\) is \([6,n]\)- panconnected except for the following four kinds of graphs and their partial graphs: \((K_ p\cup K_{n-p-2})+K_ 2\), \(K_ p+pK_ 1\), \(K_ p+((p-1)K_ 1\cup K_ 2)\), and \(K_ 3+(K_ 2\cup K_ 2\cup K_ 2)\).