# The Nonsplit Resolving Domination Polynomial of a Graph

- DOI
- 10.2991/ahis.k.210913.006How to use a DOI?
- Keywords
- Dimension of a graph, Graph polynomial, Resolving domination polynomial, Resolving dominating set
- Abstract
Metric representation of a vertex v in a graph G with an ordered subset R = {a1, a2, .., ak} of vertices of G is the k-vector r(v|R) =(d(v,a1), d(v,a2), .., d(v,ak)), where d(v,a) is the distance between v and a in G. The set R is called a Resolving set of G, if any two distinct vertices of G have distinct representation with respect to R. The cardinality of a minimum resolving in G is called a dimension of G, and is denoted by dim(G). In a graph G = (V,E), A subset D ⊆ V is a nonsplit resolving dominating set of G if it is a resolving, and nonsplit dominating set of G. The minimum cardinality of a nonsplit resolving dominating set of G is known as a nonsplit resolving domination number of G, and is represented by γnsr (G). In network reliability domination polynomial has found its application [20], a resolving set has diverse applications which includes verification of network and its discovery, mastermind game, robot navigation, problems of pattern recognition, image processing, optimization and combinatorial search [19]. Here, we are introducing nonsplit resolving domination polynomial of G. Some properties of the nonsplit Resolving domination polynomial of G are studied and nonsplit resolving domination polynomials of some well-known families of graphs are calculated.

- Copyright
- © 2021, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

### Cite this article

TY - CONF AU - N Pushpa AU - B V Dhananjayamurthy PY - 2021 DA - 2021/09/13 TI - The Nonsplit Resolving Domination Polynomial of a Graph BT - Proceedings of the 3rd International Conference on Integrated Intelligent Computing Communication & Security (ICIIC 2021) PB - Atlantis Press SP - 40 EP - 46 SN - 2589-4900 UR - https://doi.org/10.2991/ahis.k.210913.006 DO - 10.2991/ahis.k.210913.006 ID - Pushpa2021 ER -