Abstract
$\Gamma (SL_{X})$ is defined and has been investigated in (Toker, 2016). In this paper our main aim is to extend this study over $\Gamma (SL_{X})$ to the tensor product. The diameter, radius, girth, domination number, independence number, clique number, chromatic number and chromatic index of $\Gamma (SL_{X_{1}})\otimes \Gamma (SL_{X_{2}})$ has been established. Moreover, we have determined when $\Gamma (SL_{X_{1}})\otimes \Gamma (SL_{X_{2}})$ is a perfect graph.
Highlights
Let G be a graph edge set of G denoted by E(G) and vertex set of G denoted by V(G)
In this paper our main aim is to extend this study over Γ(S LX) to the tensor product
Let G1 and G2 be graphs, tensor product of G1 and G2 has vertex set V(G1) × V(G2) and has edge set {(u1, v1)(u2, v2) : u1u2 ∈ E(G1) and v1v2 ∈ E(G2)}, and it is denoted by G1 ⊗ G2
Summary
Let G be a graph edge set of G denoted by E(G) and vertex set of G denoted by V(G). Let G1 and G2 be graphs, tensor product of G1 and G2 has vertex set V(G1) × V(G2) and has edge set {(u1, v1)(u2, v2) : u1u2 ∈ E(G1) and v1v2 ∈ E(G2)}, and it is denoted by G1 ⊗ G2.
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