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The Restrained Geodetic Number of a Line Graph

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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. and Venkanagouda M Goudar. The Restrained Geodetic Number of a Line Graph. International Journal of Computer Applications 171(7):1-3, August 2017. BibTeX

@article{10.5120/ijca2017915131,
	author = {Ashalatha K. S. and Venkanagouda M. Goudar},
	title = {The Restrained Geodetic Number of a Line Graph},
	journal = {International Journal of Computer Applications},
	issue_date = {August 2017},
	volume = {171},
	number = {7},
	month = {Aug},
	year = {2017},
	issn = {0975-8887},
	pages = {1-3},
	numpages = {3},
	url = {http://www.ijcaonline.org/archives/volume171/number7/28190-2017915131},
	doi = {10.5120/ijca2017915131},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, 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

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Keywords

Cross product, Distance, Geodetic number, Line graph, Vertex covering number