Operations Research Transactions >
2023 , Vol. 27 >Issue 3: 185 - 190
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2023.03.016
Some remarks about dominating number of network
Received date: 2019-05-13
Online published: 2023-09-14
(d, w) -dominating number is an important measuring parameter for the reliability of sharing common source in a network. (1, 1) -dominating number is also known as dominating number which is a classical parameter in graph theory. (d, w) -dominating number is a simple generalization of (1, 1) -dominating number. In this paper we present a lower bound and an upper bound for the calculating of (1, w) -dominating number. Using these two bounds, we find the (1, n - 1)-dominating number and (1, n)-dominating number for hypercube, we find the (1, 2n - 1) -dominating number and (1, 2n)-dominating number for 4-ary n-cube, and the (1, n)-dominating number for n dimensional folded hypercube.
Key words： (d, w)-dominating number; hypercube; network; combinatorial problem
Jianxiu HAO . Some remarks about dominating number of network[J]. Operations Research Transactions, 2023 , 27(3) : 185 -190 . DOI: 10.15960/j.cnki.issn.1007-6093.2023.03.016
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