A note on the connectivity of Kronecker products of graphs

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Abstract

Let κ (G) be the connectivity of G. The Kronecker product G1 × G2 of graphs G1 and G2 has vertex set V (G1 × G2) = V (G1) × V (G2) and edge set E (G1 × G2) = {(u1, v1) (u2, v2) : u1 u2 ∈ E (G1) and v1 v2 ∈ E (G2)}. In this paper, we prove that κ (G × Kn) = min {n κ (G), (n - 1) δ (G)}, where G is a bipartite graph. © 2009 Elsevier Ltd. All rights reserved.

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Guji, R., & Vumar, E. (2009). A note on the connectivity of Kronecker products of graphs. Applied Mathematics Letters, 22(9), 1360–1363. https://doi.org/10.1016/j.aml.2009.03.008

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