The week's pick
Reseach Article
Permutation Labeling for some Shadow Graphs
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 40 - Number 6 |
| Year of Publication: 2012 |
| Authors: J. SHIAMA |
10.5120/4962-7224
|
J. SHIAMA . Permutation Labeling for some Shadow Graphs. International Journal of Computer Applications. 40, 6 ( February 2012), 31-35. DOI=10.5120/4962-7224
Abstract
A permutation labeling of a graph G is a bijective assignment of labels from { 1,2,3, …p} to the vertices of G such that when each edge of G has assigned a weight defined by the number of permutations of f(u) things taken f(v) at a time. Such a labeling f is called permutation labeling of G. A graph which admits permutation labeling is called permutation graphs. In this paper I proved that the shadow graphs of path Pn, star K1,n and path union of shadow graphs of cycle Cn are permutation graphs. Further I proved that the split graphs of path Pn and star K1,n are permutation graphs.
References
- B.D.Acharya and S.M .Hegde, Arithmetic graphs, J.Graph theory, 14(3) (1990),275 - 299
- L.Beineke and S.M.Hegde, Strongly multiplicative graphs , Discuss. Math. Graph theory, 21(2001), 63- 75.
- D.M.Burton, Elementary Number theory, Second edition, Wm.C.Brown Company Publishers, 1980.
- Frank Harrary, Graph theory, Narosa Publishing House- (2001).
- J A Gallian, A dynamic survey of graph labeling, The Electronics journal of Combinatories, 17(2010) # DS6
- Gary Chartrnd, Ping Zhang,Introduction to Graph theory, McGRAW- Hill International Edition
- S.C Shee Y.S Ho , “ The cardinality of path union of n copies of a graph “ , Discrete Math, 151 (1996), 221- 229
- Suresh Manjanath Hegde , Sudhakar Shetty, Combinatorial labeling of graphs ,Applied Mathematics E- notes,6(2006), 251-258© Revised 11th September
- J.Shiama” Square sum labeling for some middle and total graphs” International Journal of Computer Applications (0975-08887) Volume 37- No.4 January 2012
- J.Shiama”Permutation labeling for some split graphs” Proceedings of the National Conference on Mathematical Modelling and Simulation. NCMS’12 11th Feb.2012
- D B West, Introduction to Graph Theory, Prentice-Hall, India, 2001
Index Terms
Keywords