EDGE PRODUCT NUMBER OF CROWN GRAPH
J.P. Thavamaniet al. / IJAIR
ISSN: 2278-7844
EDGE PRODUCT NUMBER OF CROWN GRAPH
J.P.Thavamani
Department of Mathematics, M.E.S. College, Nedumkandam, Idukki, Kerala, India.
Emil: thavamaniprem@yahoo.co.in
D.S.T.Ramesh
Department of Mathematics, Margocis College, Nazareth, Tuticorin, Tamilnadu, India
Abstract
A labeling of a simple graph G is an assignment of integers to the edges subject to certain conditions. A bijection f: E P where P is a set of positive integers is called an edge function of the graph G. The smallest number r is called the edge product number G, so that G∪rK2 becomes an edge product graph. In this paper we prove some results on edge product function of wheel graph and show the existence of edge product number of crown graph.
Keywords: edge product graph, edge product number of a graph, optimal edge product function, wheel graph, crown graph.
© 2013 IJAIR. ALL RIGHTS RESERVED
264
J.P. Thavamaniet al. / IJAIR
ISSN: 2278-7844
Introduction
A renewed interest in labeling problems for graphs appears to have emanated in the mid
1960’s from a long standing conjecture of Ringel. Most graph labeling extract their origin from a paper published by Rosa in 1967[4]. Rosa introduced a labeling of a simple graph G with q edges known as β-valuation, which is an injection of the set of its vertices into the set of integers {1,2,…q} such that the values of its edges are all the numbers from 1 to q. A labeling of a graph G is an assignment of integers to the vertices or edges or both subject to certain conditions. A sum graph can be viewed as a representation of a compressed data structure. Compressed data is important in many applications involving computer memory and storage methods. Formore information and examples of the applications of graphs see
[1,3]. More on sum number and results on sum graph can be found in [2,5].
All graphs considered here are finite simple and undirected graphs. A graph is said
ISSN: 2278-7844
EDGE PRODUCT NUMBER OF CROWN GRAPH
J.P.Thavamani
Department of Mathematics, M.E.S. College, Nedumkandam, Idukki, Kerala, India.
Emil: thavamaniprem@yahoo.co.in
D.S.T.Ramesh
Department of Mathematics, Margocis College, Nazareth, Tuticorin, Tamilnadu, India
Abstract
A labeling of a simple graph G is an assignment of integers to the edges subject to certain conditions. A bijection f: E P where P is a set of positive integers is called an edge function of the graph G. The smallest number r is called the edge product number G, so that G∪rK2 becomes an edge product graph. In this paper we prove some results on edge product function of wheel graph and show the existence of edge product number of crown graph.
Keywords: edge product graph, edge product number of a graph, optimal edge product function, wheel graph, crown graph.
© 2013 IJAIR. ALL RIGHTS RESERVED
264
J.P. Thavamaniet al. / IJAIR
ISSN: 2278-7844
Introduction
A renewed interest in labeling problems for graphs appears to have emanated in the mid
1960’s from a long standing conjecture of Ringel. Most graph labeling extract their origin from a paper published by Rosa in 1967[4]. Rosa introduced a labeling of a simple graph G with q edges known as β-valuation, which is an injection of the set of its vertices into the set of integers {1,2,…q} such that the values of its edges are all the numbers from 1 to q. A labeling of a graph G is an assignment of integers to the vertices or edges or both subject to certain conditions. A sum graph can be viewed as a representation of a compressed data structure. Compressed data is important in many applications involving computer memory and storage methods. Formore information and examples of the applications of graphs see
[1,3]. More on sum number and results on sum graph can be found in [2,5].
All graphs considered here are finite simple and undirected graphs. A graph is said
References: 16(2000), 39-48 [2] Harary F, Sum graphs and difference graphs, Congress [3] Joseph J. Gallian, A guide to the graph labeling zoo, Discrete Appl. Math., 49(1994) 7 213-229 Symposium, Rome, July 1966), Gordon and Breach N.Y and Dunod Paris (1967), 349-355 [5] Singh G.S, A note on sequential crowns, Nat. Acad. Sci. Lett., 15 (1992), 193-194 [6] Thavamani J.P and Ramesh D.S.T, Edge product graph and its properties, The IUP Journal of Computational Mathematics, 4(2011), 30-38 [7] Thavamani J.P and Ramesh D.S.T, Edge product number of wheel graphs, Inter. Journal of Computing and Mathematical Applications, 5(2011), 13-20 © 2013 IJAIR