Hamiltonicity of connected domination critical graphs

© 2018 Charles Babbage Research Centre. All rights reserved. A graph G is said to be k-yc-critical if the connected domination number yc(G) of G is k and yc(G + uv) < k for every uv ? E(G). The problem of interest for a positive integer I > 2 is to determine whether or not l-connect...

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Main Authors: Kaemawichanurat, P., Caccetta, Louis, Ananchuen, W.
Format: Journal Article
Published: Charles Babbage 2018
Online Access:http://hdl.handle.net/20.500.11937/68952
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author Kaemawichanurat, P.
Caccetta, Louis
Ananchuen, W.
author_facet Kaemawichanurat, P.
Caccetta, Louis
Ananchuen, W.
author_sort Kaemawichanurat, P.
building Curtin Institutional Repository
collection Online Access
description © 2018 Charles Babbage Research Centre. All rights reserved. A graph G is said to be k-yc-critical if the connected domination number yc(G) of G is k and yc(G + uv) < k for every uv ? E(G). The problem of interest for a positive integer I > 2 is to determine whether or not l-connected k-yc-critical graphs are Hamiltonian. In this paper, for I > 2, we prove that if k - 1,2 or 3, then every l-connected k-yc-critical graph is Hamiltonian. We further show that, for n > (k - 1)k + 3, the class of i-connected Jt-yc-critical non-Hamiltonian graphs of order n is empty if and only if k = 1,2 or 3.
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spelling curtin-20.500.11937-689522018-06-29T12:27:52Z Hamiltonicity of connected domination critical graphs Kaemawichanurat, P. Caccetta, Louis Ananchuen, W. © 2018 Charles Babbage Research Centre. All rights reserved. A graph G is said to be k-yc-critical if the connected domination number yc(G) of G is k and yc(G + uv) < k for every uv ? E(G). The problem of interest for a positive integer I > 2 is to determine whether or not l-connected k-yc-critical graphs are Hamiltonian. In this paper, for I > 2, we prove that if k - 1,2 or 3, then every l-connected k-yc-critical graph is Hamiltonian. We further show that, for n > (k - 1)k + 3, the class of i-connected Jt-yc-critical non-Hamiltonian graphs of order n is empty if and only if k = 1,2 or 3. 2018 Journal Article http://hdl.handle.net/20.500.11937/68952 Charles Babbage restricted
spellingShingle Kaemawichanurat, P.
Caccetta, Louis
Ananchuen, W.
Hamiltonicity of connected domination critical graphs
title Hamiltonicity of connected domination critical graphs
title_full Hamiltonicity of connected domination critical graphs
title_fullStr Hamiltonicity of connected domination critical graphs
title_full_unstemmed Hamiltonicity of connected domination critical graphs
title_short Hamiltonicity of connected domination critical graphs
title_sort hamiltonicity of connected domination critical graphs
url http://hdl.handle.net/20.500.11937/68952