Open Neighborhood Coloring of Prisms

Swamy, Geetha Kempanapura Nanjunda; Meera, K. N.; Swamy, Narahari Narasimha; Sooryanarayana, B.

doi:10.5614/j.math.fund.sci.2013.45.3.4

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Cited by 2 publications

(2 citation statements)

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“…An antiprism graph [16] is a graph that has one of the antiprism as its skeleton. An n-sided antiprism graph has 2n vertices and 4n vertices.…”

Section: Preliminariesmentioning

confidence: 99%

Minimum Dominating Set for the Prism Graph Family

J¹

2023

Math Appl Sci Eng

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The dominating set of the graph G is a subset D of vertex set V, such that every vertex not in V-D is adjacent to at least one vertex in the vertex subset D. A dominating set D is a minimal dominating set if no proper subset of D is a dominating set. The number of elements in such set is called as domination number of graph and is denoted by $\gamma(G)$. In this work the domination numbers are obtained for family of prism graphs such as prism CL_n, antiprism Q_n and crossed prism R_n by identifying one of their minimum dominating set.

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“…An antiprism graph [16] is a graph that has one of the antiprism as its skeleton. An n-sided antiprism graph has 2n vertices and 4n vertices.…”

Section: Preliminariesmentioning

confidence: 99%

Minimum Dominating Set for the Prism Graph Family

J¹

2023

Math Appl Sci Eng

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“…These sets and dimensions have been studied for paths and cycles in [1]. Related work can be found in [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For the terms not defined here we refer to [20,22].…”

Section: Introductionmentioning

confidence: 99%

Graphs of Neighborhood Metric Dimension Two

Sooryanarayana¹,

Shanmukha

2021

J. Math. Fund. Sci.

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A subset of vertices of a simple connected graph is a neighborhood set (n-set) of G if G is the union of subgraphs of G induced by the closed neighbors of elements in S. Further, a set S is a resolving set of G if for each pair of distinct vertices x,y of G, there is a vertex s∈ S such that d(s,x)≠d(s,y). An n-set that serves as a resolving set for G is called an nr-set of G. The nr-set with least cardinality is called an nr-metric basis of G and its cardinality is called the neighborhood metric dimension of graph G. In this paper, we characterize graphs of neighborhood metric dimension two.

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Open Neighborhood Coloring of Prisms

Abstract: Abstract. For a simple, connected, undirected graph neighbor-hood coloring of the graph

Cited by 2 publications

References 13 publications

Minimum Dominating Set for the Prism Graph Family

Minimum Dominating Set for the Prism Graph Family

Graphs of Neighborhood Metric Dimension Two

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