UGC Approved Journal no 63975

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

Volume 5 Issue 7
July-2018
eISSN: 2349-5162

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

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Published Paper ID:
JETIR180Z006


Registration ID:
186027

Page Number

763-768

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Title

CONSISTENCY OF MAXIMUM PLANARITY IN RECTILINEAR CROSSING NUMBER OF COMPLETE ZERO DIVISOR GRAPH

Authors

Abstract

Let R be a commutative ring and let Z(R) be its set of zero- divisors. We associate a graph Γ(R) to R with vertices Z(R)* =Z(R) – {0}, the set of non- zero zero divisors of R and for distinct u,v Z(R)*, the vertices u and v are adjacent if and only if uv = 0 . In this paper we survey some ways of transforming a non-planar graph into a planar for complete zero divisor graphs, and discuss measures to obtain the planarity of a graph. We also characterize both the minimum and maximum number of edge crossings possible in particular Zero divisor graph classes. First we define the maximum rectilinear crossing number (MRCN) of a graph G, denoted by CR(Γ(Z_n)) where we seek a straight line drawing maximizing the number of edge crossings and secondly we recall the minimum rectilinear crossing number of zero divisor graphs especially for complete graph. Ultimately we investigate, the Maximum planar sub graphs of these maximum and minimum Rectilinear crossing number of zero divisor graphs.

Key Words

Rectilinear Crossing number, planar graph, Zero Divisor Graph

Cite This Article

"CONSISTENCY OF MAXIMUM PLANARITY IN RECTILINEAR CROSSING NUMBER OF COMPLETE ZERO DIVISOR GRAPH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 7, page no.763-768, July-2018, Available :http://www.jetir.org/papers/JETIR180Z006.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

"CONSISTENCY OF MAXIMUM PLANARITY IN RECTILINEAR CROSSING NUMBER OF COMPLETE ZERO DIVISOR GRAPH", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 7, page no. pp763-768, July-2018, Available at : http://www.jetir.org/papers/JETIR180Z006.pdf

Publication Details

Published Paper ID: JETIR180Z006
Registration ID: 186027
Published In: Volume 5 | Issue 7 | Year July-2018
DOI (Digital Object Identifier):
Page No: 763-768
Country: -, --, - .
Area: Engineering
ISSN Number: 2349-5162


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