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On the Total Vertex Irregularity Strength of Cycle Related Graphs and H-Graphs

by Indra Rajasingh, Bharati Rajan, V. Annamma
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 52 - Number 19
Year of Publication: 2012
Authors: Indra Rajasingh, Bharati Rajan, V. Annamma
10.5120/8312-1947

Indra Rajasingh, Bharati Rajan, V. Annamma . On the Total Vertex Irregularity Strength of Cycle Related Graphs and H-Graphs. International Journal of Computer Applications. 52, 19 ( August 2012), 32-37. DOI=10.5120/8312-1947

@article{ 10.5120/8312-1947,
author = { Indra Rajasingh, Bharati Rajan, V. Annamma },
title = { On the Total Vertex Irregularity Strength of Cycle Related Graphs and H-Graphs },
journal = { International Journal of Computer Applications },
issue_date = { August 2012 },
volume = { 52 },
number = { 19 },
month = { August },
year = { 2012 },
issn = { 0975-8887 },
pages = { 32-37 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume52/number19/8312-1947/ },
doi = { 10.5120/8312-1947 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:52:42.197877+05:30
%A Indra Rajasingh
%A Bharati Rajan
%A V. Annamma
%T On the Total Vertex Irregularity Strength of Cycle Related Graphs and H-Graphs
%J International Journal of Computer Applications
%@ 0975-8887
%V 52
%N 19
%P 32-37
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Let G(V, E) be a simple graph. For a labeling the weight of a vertex x is defined as = + where N(x) is the set of neighbours of x. f is called a vertex irregular total k-labeling if for every pair of distinct vertices x and y . The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G and is denoted by tvs(G). In this paper we find the total vertex irregularity strength of cycle related graphs H(n), DHF(n), F(n,2) and obtain a bound for the total vertex irregularity strength of H graphs H(k).

References
  1. Joseph A. Gallian, 2010. A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics.
  2. S. Baca, J. Jenrol, M. Miller & J. Ryan, 2007. On Irregular Total Labelings. Discrete Mathematics, vol. 307, pp. 1378-1388.
  3. Chunling. Irregular Total Labelings of some Families of Graph. Indian Journal of Pure and Applied Mathematics, to appear.
  4. J. Przybylo, 2008. Irregularity Strength of Regular Graphs. Electronic Journal of Combinatorics 15.
  5. J. Przybylo, 2008/2009. Linear Bound on the Irregularity Strength and Total Vertex Irregularity Strength of Graphs. SIAM Journal of Discrete Mathematics, 23, 511-516.
  6. Ahmaad, S. Ahtsham, Imran and A. Q. Baig. Vertex Irregular Labelings of Cubic Graphs. reprint.
  7. Wang, J. -J. , Hung, C. -N. , Tan, J. J. M. , Hsu, L. -H. and Sung T–Y, 2000. Construction Schemes for Fault Tolerant HamiltonianGraphs. Networks, 35, 233.
  8. Indra Rajasingh, Bharathi Rajan and Joice Punitha, 2007. Kernel in Cycle Related Graphs, Proceedings of the International Conference on Mathematics and Computer Science 275-278.
  9. Indra Rajasingh, Bharathi Rajan and Helda Mercy, 2009. Exact Wirelength of H Graphs on Path, Proceedings of the International Conference on Mathematics and Computer Science 275-278.
Index Terms

Computer Science
Information Sciences

Keywords

labeling vertex irregular total k-labeling total vertex irregularity strength (tvs)

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