On the Cordiality of Corona Graphs

Abstract

Let \(G_1, G_2\) be simple graphs with \(n_1, n_2\) vertices and \(m_1, m_2\) edges respectively. The Corona graph \(G_1 \circ G_2\) of \(G_1\) with \(G_2\) is obtained by taking one copy of \(G_1\), \(v_1\) copies of \(G_2\) and then joining each vertex of \(G_1\) to all the vertices of a copy of \(G_2\).

For a graph \(G\), by the index of cordiality \(i(G)\) we mean \(\min{|e_f(0)-e_f(1)|}\), where the minimum is taken over all the binary labelings of \(G\) with \(|v_f(0)-v_f(1)|\leq 1\). In this paper, we investigate the cordiality of \(G_1 \circ \overline{K_t}, K_n \circ \overline{K_t}\) and \(G \circ C_t\), where \(G\) is a graph with the index of cordiality \(k\).