首页|Domination ratio of a family of integer distance digraphs with arbitrary degree
Domination ratio of a family of integer distance digraphs with arbitrary degree
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NSTL
Elsevier
An integer distance digraph is the Cayley graph Gamma(Z, S) of the additive group Z of all integers with respect to a finite subset S subset of Z. The domination ratio of Gamma(Z, S), defined as the minimum density of its dominating sets, is related to some number theory problems, such as tiling the integers and finding the maximum density of a set of integers with missing differences. We precisely determine the domination ratio of the integer distance graph Gamma(Z, {1, 2, ..., d -2, s}) for any integers d and s satisfying d >= 2 and s is not an element of [0, d-2]. Our result generalizes a previous result on the domination ratio of the graph Gamma(Z, {1, s}) with s is an element of Z \{0, 1} and also implies the domination number of certain circulant graphs Gamma(Z(n), S), where Z(n) is the finite cyclic group of integers modulo n and S is a subset of Z(n). (C) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier
