### 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.

#### Full Text:

PDFDOI: http://dx.doi.org/10.5539/jmr.v3n3p83

Journal of Mathematics Research ISSN 1916-9795 (Print) ISSN 1916-9809 (Online)

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