International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Algebraic Structure of Graph Operations in Terms of Degree Sequences

  • Vishnu Narayan Mishra1*
  • Sadik Delen
  • Ismail Naci Cangul
  1. Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India.

* Corresponding author

Abstract

In this paper, by means of the degree sequences (DS) of graphs and some graph theoretical and combinatorial methods, we determine the algebraic structure of the set of simple connected graphs according to two graph operations, namely join and Corona product. We shall conclude that in the case of join product, the set of graphs forms an abelian monoid whereas in the case of Corona product, this set is not even associative, it only satisfies two conditions, closeness and identity element. We also give a result on distributive law related to these two operations.

How to Cite

V. N. Mishra, S. Delen, I. N. Cangul, Algebraic Structure of Graph Operations in Terms of Degree Sequences, Int. J. Anal. Appl. 16 (2018), 809–821. https://doi.org/10.28924/2291-8639-16-2018-809

BibTeX
@article{Mishra2018,
  author  = {Mishra, Vishnu Narayan and Delen, Sadik and Cangul, Ismail Naci},
  title   = {Algebraic Structure of Graph Operations in Terms of Degree Sequences},
  journal = {Int. J. Anal. Appl.},
  volume  = {16},
  year    = {2018},
  pages   = {809--821},
  doi     = {10.28924/2291-8639-16-2018-809}
}

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