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Some Domination Parameters of Arithmetic Vn Graph

by M. Manjuri, B. Maheswari
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 92 - Number 11
Year of Publication: 2014
Authors: M. Manjuri, B. Maheswari
10.5120/16054-5248

M. Manjuri, B. Maheswari . Some Domination Parameters of Arithmetic Vn Graph. International Journal of Computer Applications. 92, 11 ( April 2014), 29-32. DOI=10.5120/16054-5248

@article{ 10.5120/16054-5248,
author = { M. Manjuri, B. Maheswari },
title = { Some Domination Parameters of Arithmetic Vn Graph },
journal = { International Journal of Computer Applications },
issue_date = { April 2014 },
volume = { 92 },
number = { 11 },
month = { April },
year = { 2014 },
issn = { 0975-8887 },
pages = { 29-32 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume92/number11/16054-5248/ },
doi = { 10.5120/16054-5248 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:14:03.288978+05:30
%A M. Manjuri
%A B. Maheswari
%T Some Domination Parameters of Arithmetic Vn Graph
%J International Journal of Computer Applications
%@ 0975-8887
%V 92
%N 11
%P 29-32
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Number Theory is one of the oldest branches of mathematics, which inherited rich contributions from almost all greatest mathematicians, ancient and modern. Nathanson [1] was the pioneer in introducing the concepts of Number Theory, particularly, the 'Theory of Congruences' in Graph Theory, and paved the way for the emergence of a new class of graphs, namely "Arithmetic Graphs". Inspired by the interplay between Number Theory and Graph Theory several researchers in recent times are carrying out extensive studies on various Arithmetic graphs in which adjacency between vertices is defined through various arithmetic functions. Cayley Graphs are another class of graphs associated with elements of a group. If this group is associated with some Arithmetic function then the Cayley graph becomes an Arithmetic graph and in this paper we study the Efficient domination, Clique domination parameters of Arithmetic Vn Graphs.

References
  1. Nathanson and B. Melvyn, -Connected components of arithmetic graphs, Monat. fur. Math, 29, (1980), 219 – 220.
  2. N. Vasumath - Number theoretic graphs, Ph. D. Thesis, S. V. University, Tirupati, India. (1994).
  3. S. Uma Maheswari and B. Maheswari – Some Domination parameters of Arithmetic Graph Vn, IOSR, Journal of Mathematics, Volume 2,Issue 6,(Sep- Oct 2012), 14 -18.
  4. E. J. Cockayne, B. L. Hartnell, S. T. Hedetniemi, and R. Laskar -Efficient domination in graphs, Clemson Univ. , Dept. of Mathematical Sciences, Tech. Report, 558, (1988).
  5. M. B. Cozzens, and L. L. Kelleher - Dominating cliques in graphs, Discrete Math. 86, (1990), 101-116.
  6. G. Basco and Z. Tuza -Dominatin cliques in? P?_5 – free graphs, Period. Math. Hungar. 21, (1990), 303-308.
Index Terms

Computer Science
Information Sciences

Keywords

Arithmetic Vn Graphs Efficient domination Dominating clique Cayley Graph.

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