Product Cordial Labeling in the Context of Tensor Product of Graphs

Abstract

For the graph $G_{1}$ and $G_{2}$ the tensor product is denoted by
$G_{1}(T_{p})G_{2}$ which is the graph with vertex set
$V(G_{1}(T_{p})G_{2}) = V(G_{1}) \times V(G_{2})$ and edge set
$E(G_{1}(T_{p})G_{2})= \{(u_{1},v_{1}),(u_{2},v_{2})/u_{1}u_{2}
\epsilon E(G_{1})$ and $v_{1}v_{2} \epsilon E(G_{2})\}$. The graph
$P_{m}(T_{p})P_{n}$ is disconnected for $\forall m,n$ while the
graphs $C_{m}(T_{p})C_{n}$ and $C_{m}(T_{p})P_{n}$ are disconnected
for both $m$ and $n$ even. We prove that these graphs are product
cordial graphs. In addition to this we show that the graphs obtained
by joining the connected components of respective graphs by a path
of arbitrary length also admit product cordial labeling.