Domination and upper domination of direct product graphs

被引：10

作者：

Defant, Colin ^{[1
]}

Iyer, Sumun ^{[2
]}

机构：

[1] Princeton Univ, Princeton, NJ 08544 USA

[2] Cornell Univ, Ithaca, NY 14853 USA

来源：

DISCRETE MATHEMATICS | 2018年 / 341卷 / 10期

基金：

美国国家科学基金会;

关键词：

Domination number; Upper domination number; Direct product graph; Unitary Cayley graph; Jacobsthal's function; Balanced; Complete multipartite graph; UNITARY CAYLEY-GRAPHS; CONSECUTIVE PRIMES; LARGE GAPS;

D O I：

10.1016/j.disc.2018.06.031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X-z/nz denote the unitary Cayley graph of Z/nZ. We present results on the tightness of the known inequality gamma (X-z/nz) <= gamma(t)(X-z/nz) <= g(n), where gamma and gamma(t) 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 gamma(X-z/nz) <= gamma(t) (X-z/nz) <= g(n) - 1. 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. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：2742 / 2752

页数：11