The Transversal Neighborhood Domination Number on Parachute Graph and Semi-Parachute Graph

DOI

10.2991/978-94-6463-228-6_38How to use a DOI?

Keywords

Domination Set; Neighborhood Set; Neighborhood Transversal Dominating Set; Parachute Graph; Semi-parachute Graph

Abstract

Given V be a set of vertices on a graph G. A set D ⊆ V, is dominating set of G = (V, E) if all the vertex that is not in the set D are neighbors to at least one vertex of D. The smallest number of elements in D is known as the domination number. A set D ⊆ V(G) is called a transversal neighborhood-dominating set if D is the dominating set of G and intersects with every minimum neighborhood set. The transversal neighborhood domination number of G is the smallest number of elements in each transversal neighborhood-dominating set.. In this paper, we discuss transversal neighborhood domination number on a parachute graph and a semi-parachute graph. The transversal neighborhood domination number on parachute graph is (n + 3)/3 for every n = 3 k, (n + 5)/3 for every n = 3 k + 1, and (n + 4)/3 for every n = 3 k + 2. The neighborhood transversal domination number on the semi-parachute graph is (n + 1)/2 for every n = 2 k + 1 and (n + 2)/2 for every n = 2 k.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Fransiskus Fran
AU  - Nilamsari Kusumastuti
AU  - Yuni Elisa
AU  - Steven
PY  - 2023
DA  - 2023/08/22
TI  - The Transversal Neighborhood Domination Number on Parachute Graph and Semi-Parachute Graph
BT  - Proceedings of the 4th International Seminar on Science and Technology (ISST 2022)
PB  - Atlantis Press
SP  - 339
EP  - 348
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-228-6_38
DO  - 10.2991/978-94-6463-228-6_38
ID  - Fran2023
ER  -