Advances and Applications in Discrete Mathematics
Volume 21, Issue 2, Pages 139 - 162
(July 2019) http://dx.doi.org/10.17654/ |
|
ON 2-POINT-SET DOMINATING SETS
Salma L. Naga-Marohombsar and Ferdinand P. Jamil
|
Abstract: A set S of vertices of a connected graph G is a 2-point-set dominating set if for every there is a nonempty containing at most two vertices such that the induced subgraph of G is connected. If, in addition, for every there is a adjacent to u for which is a 2-point-set dominating set of G, then S is a secure 2-point-set dominating set. This paper initiates the study of secure 2-point-set domination in graphs. It characterizes 2-point-set dominating sets and secure 2-point-set dominating sets in both the join and corona of graphs, and, as a result, determines the values of their respective corresponding point-set domination invariants. |
Keywords and phrases: 2-point-set dominating set, secure 2-point-set dominating set, 2-point-set domination number, secure 2-point-set domination number.
|
|
Number of Downloads: 268 | Number of Views: 1854 |
|