Independent Number and Dominating Number of (n,k)-Star Graphs

Wei, Yunchao; Chen, Fuguang; Zhu, Hongxian

doi:10.11591/telkomnika.v11i1.1901

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Cited by 4 publications

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“…The above I k is constructed in Wei's paper [18]. However, their construction is wrong and without detailed proof.…”

Section: Preliminary Resultsmentioning

confidence: 99%

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Maximum Independent Sets Partition of (n, k)‐Star Graphs

2019

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The (n, k)-star graph is a very important computer modelling. The independent number and chromatic number of a graph are two important parameters in graph theory. However, we did not know the values of this two parameters of the (n, k)-star graph since it was proposed. In [18], Wei et. al. declared that they determined the independent number of the (n, k)-star graph, unfortunately their proof is wrong. This paper generalize their result and present a maximum independent sets partition of (n, k)-star graph. From that we can immediately deduce the exact value of the independent number and chromatic number of (n, k)-star graph.

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“…The above I k is constructed in Wei's paper [18]. However, their construction is wrong and without detailed proof.…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…The independent number and chromatic number of a graph are two important parameters in graph theory. In [18], Wei et. al.…”

Section: Introductionmentioning

confidence: 99%