Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902854 | Discrete Mathematics | 2018 | 11 Pages |
Abstract
Let XZânZ denote the unitary Cayley graph of ZânZ. We present results on the tightness of the known inequality γ(XZânZ)â¤Î³t(XZânZ)â¤g(n), where γ andγt denote the domination number and total domination number, respectively, and g is the arithmetic function known as Jacobsthal's function. In particular, we construct integers n with arbitrarily many distinct prime factors such that γ(XZânZ)â¤Î³t(XZânZ)â¤g(n)â1. We give lower bounds for the domination numbers of direct products of complete graphs and present a conjecture for the exact values of the upper domination numbers of direct products of balanced, complete multipartite graphs.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Colin Defant, Sumun Iyer,