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

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 $G \times C_{2n+1}$.