Resolving domination number of helm graph and it’s operation

Abstract

Let G be a connected graph. Dominating set is a set of vertices which each vertex D has at least one neighbor in G. The minimum cardinality of D is called the domination number G(γ(G)). The metric dimension of G is the minimum cardinality of a series of vertices so that each vertex G is uniquely. It is determined by the distance of vector to the selected vertices. A dominating metric dimension set is a set of vertices has a dominating set D which has condition of metric dimension. The minimum cardinality is called the resolving domination number of G, (DomDim (G)). We analyze the resolving domination number of helm graph and it’s operation. We study combine the existence concept of dominating set and metric dimension. We have obtained the minimum cardinality of dominating number.

On the resolving strong domination number of some wheel related graphs

“…To construct the theorem of this case, firstly we show the lower bound of γ rst (H n ) for n = 3 and n = 4 by Lemma 1. Based on [14] dim(H n ) = n, n ≤ 3, and based on Theorem 1 γ st (H n ) = n, for n = 3 and n = 4, so we have γ rst (H n ) ≥ max{γ st (H n ), dim(H n )} = max{n, n} = n. Secondly, we suppose D s = {xi : 1 ≤ i ≤ n} as a resolving strong dominating set of (H n ). We show the representations of all vertices of H 3 and H 4 which require the resolving strong dominating set in the following.…”

“…Same with the proof of Case 1, firstly we show the lower bound of γ rst (H n ) for n otherwise by Lemma 1. Based on Hayyu et al [14] dim(H n ) = n, n ≤ 3, and based on Theorem 3.…”

Integrating Ecological Forecasting into Undergraduate Ecology Curricula with an R Shiny Application-Based Teaching Module

“…Another example of an interactive online tool is the common online data analysis platform (CODAP), which has been integrated into the teaching of machine learning and other data science topics [28]. Interactive activities embedded in online applets facilitate students learning at their own pace, and self-discovery has been shown to improve students' understanding and ability to retain information [29,30].…”

On resolving efficient domination number of path and comb product of special graph

“…The resolving domination number is its minimum cardinality and denoted by γ r G. A resolving dominating set of graph G is a subset Y of V (G) which is not only a ominating set of G but also determine every vertex of G by its distance representation in respect to every vertex in Y . We refer to [1,21,23,34] for some previous results. Several types of resolving domination number are resolving strong domination number, resolving perfect domination number, and resolving efficient domination number, see [28,24].…”