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Super Connected Kronecker Products of Paths, Cycles and Cycles

School of Mathematics and System Sciences, Xinjiang University, Urumqi Xinjiang 830017, China
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Abstract

A graph G is super connected, or simply super-κ, if every minimum vertex-cut isolates a vertex. The Kronecker product G1 × G2 of graphs G1 and G2 is the graph with vertex set V (G1 × G2) = V(G1) × V (G2) and edge set E(G1 × G2) = {(u1,v1)(u2,v2): u1u2 ∈ E(G1),v1v2 ∈ E(G2)}. In this paper, we prove that Pm × Cn is super-κ for m≥4, n≥3 and n is odd; Cm × Cn is super-κ for m≥5, n≥3 and n is odd.

Keywords

Kronecker productconnectivitymaximal connectednesssuper connectedness
CLC number: O157.5 Document code: A Article ID: 2096-7675(2022)02-0176-06

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Journal of Xinjiang University(Natural Science Edition in Chinese and English)
Volume 39 Issue 2,
March 2022
Pages 176-181
DOI: 10.13568/j.cnki.651094.651316.2021.02.17.0001

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Cite this article:
WU L, TIAN Y. Super Connected Kronecker Products of Paths, Cycles and Cycles. Journal of Xinjiang University(Natural Science Edition in Chinese and English), 2022, 39(2): 176-181. https://doi.org/10.13568/j.cnki.651094.651316.2021.02.17.0001

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Received: 17 February 2021
Published: 01 March 2022
© 2022 Journal of Xinjiang University (Natural Science Edition in Chinese and English)