Cordial labeling and arbitrary super subdivision of some graphs (Q2920094)

A binary vertex labelling \(f\) of a graph \(G\) is called a \textit{cordial labelling} if \(|v_f(0)-v_f(1)|\leq1\) and \(|e_f(0)-e_f(1)|\leq1\), where \(v_f(i)\), \(e_f(i)\) denote the number of vertices and edges, respectively, having labels \(i\).NEWLINENEWLINEA \textit{super subdivision} of graph \(G\) is obtained from \(G\) by replacing every edge \(e_i\) with a complete bipartite graph \(K_{2,m_i}\) s.t. the end vertices of \(e_i\) are identified with the two vertices of 2-vertices part of \(K_{2,m_i}\).NEWLINENEWLINEThe main contribution of the paper is a constructive proof that the graphs obtained by arbitrary super subdivisions of a tree, grid graph, complete bipartite graph and \(C_n\odot P_m\) for some restricted \(m, n\) are cordial.