UGC Approved Journal no 63975

ISSN: 2349-5162 | ESTD Year : 2014
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Published in:

Volume 6 Issue 2
February-2019
eISSN: 2349-5162

UGC and ISSN approved 7.95 impact factor UGC Approved Journal no 63975

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Published Paper ID:
JETIREL06049


Registration ID:
305890

Page Number

255-260

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Title

On Equitable Power Domination Number of Some Graphs

Abstract

Let G (V, E) be graph. A set S ⊆ V is said to be a power dominating set (PDS) if every vertex u ∈ V-S is observed by certain vertices in S by the following rules: (i) if a vertex v in G is in PDS, then it dominates itself and all the adjacent vertices of v and (ii) if an observed vertex v in G has k > 1 adjacent vertices and if k-1 of these vertices are already observed, then the remaining one non-observed vertex is also observed by v in G. A power dominating set S ⊆ V in G (V,E) is said to be an equitable power dominating set (EPDS), if for every vertex v ∈ V-S there exists an adjacent vertex u ∈ S such that the difference between the degree of u and degree of v is less than or equal to 1, i.e., |d(u)-d(v)|≤ 1. The minimum cardinality of an equitable power dominating set of G is called the equitable power domination number of G, denoted by γ_epd (G). “An edge is said to be subdivided if the edge xy is replaced by the path: xwy, where w is the new vertex. A graph obtained by subdividing each edge of a graph G is called subdivision of G, and is denoted by S(G)". In this paper we establish the equitable power domination number of subdivision of graphs. We also obtain the equitable power domination number of the generalized Petersen graphs and balanced binary tree.

Key Words

Power dominating set, Power domination number, Equitable power dominating set, Equitable power domination number, Generalized Petersen graphs, Balanced binary tree, and Subdivision graph.

Cite This Article

"On Equitable Power Domination Number of Some Graphs", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 2, page no.255-260, February-2019, Available :http://www.jetir.org/papers/JETIREL06049.pdf

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2349-5162 | Impact Factor 7.95 Calculate by Google Scholar

An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 7.95 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator

Cite This Article

"On Equitable Power Domination Number of Some Graphs", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 2, page no. pp255-260, February-2019, Available at : http://www.jetir.org/papers/JETIREL06049.pdf

Publication Details

Published Paper ID: JETIREL06049
Registration ID: 305890
Published In: Volume 6 | Issue 2 | Year February-2019
DOI (Digital Object Identifier):
Page No: 255-260
Country: Phagwara, Punjab, India .
Area: Applied Mathematics
ISSN Number: 2349-5162


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