Independence number and connectivity of maximal connected domination vertex critical graphs

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Publication Details

Author list: Kaemawichanurat P.; Almalki N.

Publisher: Azarbaijan Shahid Madani University

Publication year: 2024

Volume number: 9

Issue number: 2

Start page: 185

End page: 196

Number of pages: 12

ISSN: 538-2128

eISSN: 2538-2136

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85185305229&doi=10.22049%2Fcco.2023.28629.1639&partnerID=40&md5=76fbff19be69f50d91fb23cac0550a21

Languages: English-Great Britain (EN-GB)

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Abstract

A k-CEC graph is a graph G which has connected domination number γc(G) = k and γc(G+uv) < k for every uv ∈ E(G). A k-CVC graph G is a 2-connected graph with γc(G) = k and γc(G − v) < k for any v ∈ V (G). A graph is said to be maximal k-CVC if it is both k-CEC and k-CVC. Let δ, κ, and α be the minimum degree, connectivity, and independence number of G, respectively. In this work, we prove that for a maximal 3-CVC graph, if α = κ, then κ = δ. We additionally consider the class of maximal 3-CVC graphs with α < κ and κ < δ, and prove that every 3-connected maximal 3-CVC graph when κ < δ is Hamiltonian connected. © 2024 Elsevier B.V., All rights reserved.

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