# Some Results on Tensor Product of a Graph and an Odd Cycle

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## Abstract

The *tensor product* \(G \times H\) of two graphs *G* and *H* is a graph such that the vertex set of \(G \times H\) is the cartesian product \(V(G) \times V(H)\) and two vertices \((u_1, u_2)\) and \((v_1, v_2)\) are adjacent in \(G \times H\) if and only if \(u_1\) is adjacent to \(v_1\) in *G* and \(u_2\) is adjacent to \(v_2\) in *H*. In this paper, we establish a structural characterization of \(G \times C_{2n+1}\). Further, we discuss Eulerian, Hamiltonian and planar properties of \(G \times C_{2n+1}\).

## Keywords

Tensor product of graphs Decomposable graphs Eulerian graphs Hamiltonian graphs Planar graphs## Mathematics Subject Classification

05C75 05C76## Notes

### Acknowledgements

The authors express their gratitude to Prof. E. Sampathkumar who in his early research has brought up the idea of tensor product of the particular graphs which on reading gave us an instant insight to go for \(G \times C_{2n+1}\) and admire the beauty of traversability and many interesting properties of the structure.

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