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Independence number and connectivity of maximal connected domination vertex critical graphs.
- Source :
-
Communications in Combinatorics & Optimization . 2024, Vol. 9 Issue 2, p185-196. 12p. - Publication Year :
- 2024
-
Abstract
- A k -CEC graph is a graph G which has connected domination number Yc(G) = k and Yc(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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 25382128
- Volume :
- 9
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Communications in Combinatorics & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 175588549
- Full Text :
- https://doi.org/10.22049/cco.2023.28629.1639