THE FORCING NONSPLIT DOMINATION NUMBER OF A GRAPH

被引:1
|
作者
John, J. [1 ]
Raj, Malchijah [2 ]
机构
[1] Govt Coll Engn, Dept Math, Tirunelveli 627007, India
[2] Bharathiar Univ, Res & Dev Ctr, Coimbatore 641046, Tamil Nadu, India
来源
KOREAN JOURNAL OF MATHEMATICS | 2021年 / 29卷 / 01期
关键词
dominating set; domination number; forcing domination number; non-split domination number; forcing non-split domination number;
D O I
10.11568/kjm.2021.29.1.1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A dominating set S of a graph G is said to be nonsplit dominating set if the subgraph < V - S > is connected. The minimum cardinality of a nonsplit dominating set is called the nonsplit domination number and is denoted by gamma(ns) (G). For a minimum nonsplit dominating set S of G, a set T subset of S is called a forcing subset for S if S is the unique gamma(ns)-set containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing nonsplit domination number of S, denoted by f(gamma ns )(S), is the cardinality of a minimum forcing subset of S. The forcing nonsplit domination number of G, denoted by f(gamma ns) (G) is defined by f(gamma ns) (G) = min{f(gamma ns) (S)} , where the minimum is taken over all gamma(ns)-sets S in G. The forcing nonsplit domination number of certain standard graphs are determined. It is shown that, for every pair of positive integers a and b with 0 <= a <= b and b >= 1, there exists a connected graph G such that f(gamma ns )(G) = a and gamma(ns) (G) = b. It is shown that, for every integer a >= 0, there exists a connected graph G with f(gamma) (G) = f(gamma ns) (G) = a, where f(gamma)(G) is the forcing domination number of the graph. Also, it is shown that, for every pair a, b of integers with a >= 0 and b >= 0 there exists a connected graph G such that f(gamma )(G) = a and f(gamma ns)(G) = b.
引用
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页码:1 / 12
页数:12
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