Non Split Geodetic Number of a Line Graph

Ashalatha K.S; Venkanagouda M Goudar; Venkatesha

Non Split Geodetic Number of a Line Graph

Ashalatha K.S * §

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Venkanagouda M Goudar

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Venkatesha

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Kuvempu University

Non Split Geodetic Number of a Line Graph

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Abstract

A set S V [L(G)] is a non split geodetic set of L(G), if S is a geodetic set and is connected. The non split geodetic number of a line graph L(G), is denoted by g [L(G)], is the minimum cardinality of a non split geodetic set of L(G). In this paper we obtain the non split geodetic number of line graph of any graph. Also obtain many bounds on non split geodetic number in terms of elements of G and covering number of G. We investigate the relationship between non split geodetic number and geodetic number.

References

7 Cites in Article

Reference Format

w 2 } forms minimum geodetic set of L(K 2 × P 2 ). Consider H = {u 2 , w 1 } ⊆ V -S. Now S = S ∪ {w 1 } or {u 2 }, where w 1 , u 2 are isolated vertices in V -S forms minimum non split geodetic set of L(K 2 × P 2 ).
w 1 , w 3 } forms minimum geodetic set of L(K 2 × P 3 ).
Gary Chartrand,Frank Harary,Ping Zhang (2002). On the geodetic number of a graph.
G Chartrand,P Zhang (2006). Introduction to Graph Theory.
Frank Harary (1969). GRAPH THEORY.
M Venkanagouda,K Goudar,Ashalatha,M Venkatesha (2012). On the Geodetic Number of Line Graph.
M Venkanagouda,Tejaswini Goudar,Venkatesha Non Split Geodetic Number of a Graph.

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Ashalatha K.S, Venkanagouda M Goudar, Venkatesha. 2014. "Non Split Geodetic Number of a Line Graph". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 13 (GJSFR Volume 13 Issue F11).

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GJSFR Volume 13 Issue F11

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

cartesian product distance edge covering number line graph non split geodetic number vertex covering number

Classification

GJSFR-F Classification MSC 2010: 05C05

05C12

Submission ReceivedNovember 19, 2013
Peer Review Double Blind
Handling Editor
Accepted December 13, 2013
Published December 23, 2013

Version of record

v1.2

Issue date

March 22, 2014

Language

English

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Article Matrices

Total Score: 147

Country: India

Subject: Global Journal of Science Frontier Research

Authors: Ashalatha K.S, Venkanagouda M Goudar, Venkatesha (PhD/Dr. count: 0)

View Count (all-time): 312

Total Views (Real + Logic): 1134

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Publish Date: 2013 12, Mon

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Total Views: 1.1K

Total Downloads: 78

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