Graphs and Degree Equitability

DOI: 10.4236/am.2013.48160   PDF   HTML     2,705 Downloads   4,079 Views   Citations

Abstract

Let G=(V,E)  be a graph. If φ is a function from the vertex set V(G) to the set of positive integers. Then two vertices u, v ∈ V(G)  are φ -equitable if|φ(u)-φ(v)|≤1.By the degree, equitable adjacency between vertices can be redefine almost all of the variants of the graphs. In this paper we study the degree equitability of the graph by defining equitable connectivity, equitable regularity, equitable connected graph and equitable complete graph. Some new families of graphs and some interesting results are obtained.


Share and Cite:

A. Al-Kenani, N. Soner and A. Alwardi, "Graphs and Degree Equitability," Applied Mathematics, Vol. 4 No. 8, 2013, pp. 1199-1203. doi: 10.4236/am.2013.48160.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] [1] F. Harary, “Graph Theory,” Addison-Wesley, Reading, 1969.
[2] [2] V. Swaminathan and K. M. Dharmalingam, “Degree Equitable Domination on Graphs,” Kragujevac Journal of Mathematics, Vol. 35, No. 1, 2011, pp. 191-197.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.