Product Cordial Labelling for Some Bicyclic Graphs

Abstract

A graph \(G\) with lines and points is known as a product cordial graph if there occurs a labeling \(g\) from \(V(G)\) to \(\{0,1\}\) such that if every line \(rt\) is given the labeled \(g(r) .g(t)\), then the cardinality of points with labeled zero and the cardinality of points with labeled one vary as a maximum by one and the cardinality of lines with labeled zero and the cardinality of lines with labeled one vary by as a maximum one. In this case, \(g\) is alleged the product cordial labeling of \(G\). This paper deals with product cordial labeling for some graphs related to bicyclic graph such as \(B[n,n]\), \(B[n,n]*S_m\), \(B[n,n]*P_2*S_m\) and \(B[n,n]*P_3*S_m\), \(B[n,n] \odot K_2\), \(B[n,n] \odot K_3\).