The $ (a, d) $-ascending subgraph decomposition

Authors

  • A. Nagarajan
  • S. Navaneetha Krishnan

DOI:

https://doi.org/10.5556/j.tkjm.37.2006.151

Abstract

Let $ G $ be a graph of size $ q $ and $ a $, $ n $, $ d $ be positive integers for which $ \frac{n}{2}(2a+(n-1)d)\le q<(\frac{n+1}{2})(2a+nd) $. Then $ G $ is said to have $ (a, d) $- ascending subgraph decomposition into $ n $ parts $ ((a, d)- ASD) $ if the edge set of $ G $ can be partitioned into $ n $-non-empty sets generating subgraphs $ G_1 $, $ G_2 $, $ G_3 $, $ \ldots $, $ G_n $ without isolated vertices such that each $ G_i $ is isomorphic to a proper subgraph of $ G_{i+1} $ for $ 1\le i\le n-1 $ and $ |E(G_i)|=a+(i-1)d $. In this paper, we find $ (a, d)-ASD $ into $ n $ parts for $ W_m $.

Author Biographies

A. Nagarajan

Department of Mathematics, V.O.C. College, Tuticorin-628008, Tamilnadu, India.

S. Navaneetha Krishnan

Department of Mathematics, V.O.C. College, Tuticorin-628008, Tamilnadu, India.

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Published

2006-12-31

How to Cite

Nagarajan, A., & Krishnan, S. N. (2006). The $ (a, d) $-ascending subgraph decomposition. Tamkang Journal of Mathematics, 37(4), 377-390. https://doi.org/10.5556/j.tkjm.37.2006.151

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Papers