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THE EXISTENCE OF ARBITRARILY TOUGH AND TRIANGLE- FREE GRAPHS
Subject area: Science,Engineering and Technology · Area of research: Mathemetics
Abstract
In this paper we mention vertex connectivity and independence number. We establish that every hamiltonian graph and any Gl graph are 1-tough. And then, we describe the bound of the toughness t(G) in terms of independence number 𝛃(G) and the number of vertices, n in G. Finally, a 1- tough graph Gl, it is shown that and the result reveals that a triangle- free graph with are obtained.
Keywords
connectivity, independence number, minimum degree, layers of G, 1-tough, Hamiltonian graph, complete bipartite, triangle-free graph.
References
[1] Bollobas , B ., “ Modern Graph Theory ”, Springer - Verlag, New York, 1998
[2] Bondy, J .A . and Murty, U .S .R ., “Graph Theory with App lications”, The Macmillan Press Ltd , London , 1976 .
[3] hartrand, G. and Lesniak. L., “Graphs and Digraphs”, Chapman and Hall/CRC, New York, 2005 .
[4] Grossman , J . W., “Discrete Mathematics”, Macmillan Publishing Company, New York, 1990 .
[5] D.Bauer, J.Van Den Heuvel and E.Schemeichel, “Toughess and Triangle- Free Graphs”, paper presented in the Department of Mathematics and Computer Science, San Jose State University, San Jose Califonia. April, 21, 1993.
How to cite this paper
@article{1701503,
author = {San San Tint, Khaing Khaing Soe Wai},
title = {THE EXISTENCE OF ARBITRARILY TOUGH AND TRIANGLE- FREE GRAPHS},
journal = {Iconic Research And Engineering Journals},
year = {2019},
volume = {3},
number = {2},
pages = {238-243},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1701503.pdf},
abstract = {In this paper we mention vertex connectivity and independence number. We establish that every hamiltonian graph and any Gl graph are 1-tough. And then, we describe the bound of the toughness t(G) in terms of independence number 𝛃(G) and the number of vertices, n in G. Finally, a 1- tough graph Gl, it is shown that and the result reveals that a triangle- free graph with are obtained.},
keywords = {connectivity, independence number, minimum degree, layers of G, 1-tough, Hamiltonian graph, complete bipartite, triangle-free graph.},
month = {August},
}