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 $B[n,n]$, $B[n,n]\ast S_m$, $B[n,n]\ast P_2\ast S_m$ and $B[n,n]\ast P_3\ast S_m$, $B[n,n]\odot K_2$, $B[n,n]\odot K_3$.