Product Cordial Labeling in the Context of Tensor Product of Graphs
Samir K. VAIDYA, Nikhil Vyas · Journal of Mathematics Research · 2011
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 thegraphs $C_{m}(T_{p})C_{n}$ and $C_{m}(T_{p})P_{n}$ are disconnectedfor both $m$ and $n$ even. We prove that these graphs are productcordial graphs. In addition to this we show that the graphs obtainedby joining the connected components of respective graphs by a pathof arbitrary length also admit product cordial labeling.