Research Article
Generating the Vertex Sets with some Distance Parameter Properties in Caterpillar Graphs
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 84 - Issue 1 |
| Published: December 2013 |
| Authors: Shreedevi V. Shindhe, Ishwar. B, Marriswamy. R |
10.5120/14538-2613
|
Shreedevi V. Shindhe, Ishwar. B, Marriswamy. R . Generating the Vertex Sets with some Distance Parameter Properties in Caterpillar Graphs. International Journal of Computer Applications. 84, 1 (December 2013), 6-8. DOI=10.5120/14538-2613
@article{ 10.5120/14538-2613,
author = { Shreedevi V. Shindhe,Ishwar. B,Marriswamy. R },
title = { Generating the Vertex Sets with some Distance Parameter Properties in Caterpillar Graphs },
journal = { International Journal of Computer Applications },
year = { 2013 },
volume = { 84 },
number = { 1 },
pages = { 6-8 },
doi = { 10.5120/14538-2613 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2013
%A Shreedevi V. Shindhe
%A Ishwar. B
%A Marriswamy. R
%T Generating the Vertex Sets with some Distance Parameter Properties in Caterpillar Graphs%T
%J International Journal of Computer Applications
%V 84
%N 1
%P 6-8
%R 10.5120/14538-2613
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In this paper the vertices of caterpillar tree T are viewed with different approach and categorized into the sets D, R and X, based on the distance parameters i. e. , diameter and radius. The distance parameters have been presented with some set theory views. Here D is the set of diametral vertices, R is the set of central vertices and X is the set of vertices which are neither central nor peripheral. Then, |D|+|R|+|X|=n. The cardinality of these sets has some property and helps to specify the basic characters of caterpillar tree. A linear complexity algorithm is also designed to generate these sets.
References
- Distance in graphs - Fred Buckley, Frank Harary, Addison-Wesley Pub. Co. , ©1990 .
- Harary. F, Graph Theory, Addison Wesley.
- Coremen. T. H, Leiserson, C. E. Rivest R. L, and C Stein, Introduction to Algorithms, 2nd Ed. MIT press, Cambridge, MA, 2001.
- Fundamentals of Computer Algorithms, E. Horowitz, S. Sahni, S. Rajasekharan, Universities Press, 2009.
- Data Structures, Algorithms, and Applications in C++, Sartaj Sahni. McGraw-Hill Education, 1998.
- Shreedevi V. Shindhe, Ph. D thesis, "Algorithmic aspects of distance based parameters", Karnatak University, Dharwad, 2012.
- H. B. Walikar, Shreedevi V. Shindhe , Ishwar Baidari - DRI of a vertex, Self Centered Graphs and Almost Self Centered Graphs - An algorithmic approach,(152-156) International Journal of Computer Applications, Issue. 2, Vol. 4 August 2012.
- Sandi KLAVZAR, Kishori P. NARAYANKAR and H. B. WALIKAR -Almost Self-Centered Graphs, Acta Mathematica Sinica, English Series, Dec. , 2011, Vol. 27, No. 12, pp. 2343–2350.
- Discrete Mathematics and its Applications, Kenneth H. Rosen, 6th Ed, Tata McGraw-Hill, 2007.
- Discrete Mathematical Structures- Kolman, Busby, Ross, 5th Ed, PHI, 2000.
Index Terms
Keywords