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Reseach Article

The Restrained Geodetic Number of a Line Graph

by Ashalatha K. S., Venkanagouda M. Goudar
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 171 - Number 7
Year of Publication: 2017
Authors: Ashalatha K. S., Venkanagouda M. Goudar
10.5120/ijca2017915131

Ashalatha K. S., Venkanagouda M. Goudar . The Restrained Geodetic Number of a Line Graph. International Journal of Computer Applications. 171, 7 ( Aug 2017), 1-3. DOI=10.5120/ijca2017915131

@article{ 10.5120/ijca2017915131,
author = { Ashalatha K. S., Venkanagouda M. Goudar },
title = { The Restrained Geodetic Number of a Line Graph },
journal = { International Journal of Computer Applications },
issue_date = { Aug 2017 },
volume = { 171 },
number = { 7 },
month = { Aug },
year = { 2017 },
issn = { 0975-8887 },
pages = { 1-3 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume171/number7/28190-2017915131/ },
doi = { 10.5120/ijca2017915131 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:19:07.486654+05:30
%A Ashalatha K. S.
%A Venkanagouda M. Goudar
%T The Restrained Geodetic Number of a Line Graph
%J International Journal of Computer Applications
%@ 0975-8887
%V 171
%N 7
%P 1-3
%D 2017
%I Foundation of Computer Science (FCS), NY, USA
Abstract

For any graph G(V,E), the line graph of G denoted by L(G). The Line graph L(G) whose vertices corresponds to the edges of G and two vertices in L(G) are adjacent if and only if the corresponding edges in G are adjacent. A geodetic set S ⊆ V (G) of a graph G = (V,E) is a restrained geodetic set if the subgraph V-S has no isolated vertex. The minimum cardinality of a restrained geodetic set is the restrained geodetic number. In this paper we obtained the restrained geodetic number of line graph of any graph. Also, obtained many bounds on restrained geodetic number in terms of elements of G and covering number of G.

References
  1. F Buckley and F. Harary. Distance in graphs, Addison-Wesely, Reading, MA (1990).
  2. G. Chartrand, F. Harary, and P.Zhang. Geodetic sets in graphs Discussiones Mathematicae Graph Theory 20 (2000), 129-138.
  3. G. Chartrand, F. Harary, H.C Swart and P.Zhang. Geodomination in graphs, Bull. ICA 31 (2001), 51-59.
  4. G. Chartrand, F. Harary, and P.Zhang. On the geodetic number of a graph.Networks.39 (2002) 1-6.
  5. G. Chartrand and P.Zhang. Introduction to Graph Theory, Tata McGraw Hill Pub.Co.Ltd.(2006).
  6. F.Harary, Graph Theory, Addison-Wesely, Reading, MA, 1969.
Index Terms

Computer Science
Information Sciences

Keywords

Cross product Distance Geodetic number Line graph Vertex covering number