On the Cordiality of \(D(1, 3)\) Graphs

Abstract

Let \(d_G(v)\) be the degree of a vertex \(v\) in a graph \(G\). A graph \(G\) is called a \(D(i_1, \ldots,i_k)\) graph, if \(\{d_G(v) \mid x \in V(G)\} = \{i_1, \ldots, i_k\}\). In this paper, a necessary and sufficient condition for a connected \(D(1, 3)\) graph to be cordial is given.