UGC Approved Journal no 63975(19)

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Volume 6 Issue 1
January-2019
eISSN: 2349-5162

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

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Published Paper ID:
JETIRDY06116


Registration ID:
232843

Page Number

724-729

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Title

On Divisor 3-Equitable Labeling of Certain Graphs

Abstract

An assignment of integers to the vertices of a graph G is called a vertex labeling of G. The concept of graph labeling plays a vital role in computer and network security. A graph G on n vertices is said to admit a divisor 3-equitable labeling if there exists a bijection d∶V(G)→ {1,2,...,n} defined by d (e=xy)={█(1,ifd(x)|d(y)" or" d(y)|d(x)@2, if d(x)/d(y) =2 or d(y)/d(x) =2@0, otherwise)┤ and |e_d (i)-e_d (j)|≤ 1 for all 0 ≤ i,j≤ 2. A graph which permits a divisor 3-equitable labeling is called a divisor 3-equitable graph. A graph K_n in which “every pair of vertices is adjacent” is called a complete graph and a complete bipartite graph K_(1,n) is known as a star graph. In this paper, we prove the non-existence of a divisor 3-equitable labeling of the complete graph K_n for n≥5 and star graph K_(1,n) for n≥6.

Key Words

3-equitable labeling, divisor 3-equitable labeling, complete graph, star graph

Cite This Article

"On Divisor 3-Equitable Labeling of Certain Graphs", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 1, page no.724-729, January 2019, Available :http://www.jetir.org/papers/JETIRDY06116.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 Divisor 3-Equitable Labeling of Certain Graphs", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 1, page no. pp724-729, January 2019, Available at : http://www.jetir.org/papers/JETIRDY06116.pdf

Publication Details

Published Paper ID: JETIRDY06116
Registration ID: 232843
Published In: Volume 6 | Issue 1 | Year January-2019
DOI (Digital Object Identifier):
Page No: 724-729
Country: -, -, - .
Area: Engineering
ISSN Number: 2349-5162
Publisher: IJ Publication


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