Vulnerability Parameters of Tensor Product of Complete Equipartite Graphs


Let G1 and G2 be two simple graphs. The tensor product of G1 and G2, denoted by G1 × G2, has vertex set V (G1 × G2) = V (G1) × V (G2) and edge set E(G1 × G2) = {(u1, v1)(u2, v2) : u1u2 ∈ E(G1) and v1v2 ∈ E(G2)}. In this paper, we determine vulnerability parameters such as toughness, scattering number, integrity and tenacity of the tensor product of the graphs Kr(s) × Km(n) for r ≥ 3,m ≥ 3, s ≥ 1 and n ≥ 1, where Kr(s) denotes the complete r-partite graph in which each part has s vertices. Using the results obtained here the theorems proved in [Aygul Mamut, Elkin Vumar, Vertex Vulnerability Parameters of Kronecker Products of Complete Graphs, Information Processing Letters 106 (2008), 258–262] are obtained as corollaries.

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@inproceedings{Paulraja2013VulnerabilityPO, title={Vulnerability Parameters of Tensor Product of Complete Equipartite Graphs}, author={P. Paulraja and Sheeba Agnes and Dalibor Froncek}, year={2013} }