Connectivity of The Mycielskian of A Graph

Authors

  • Mr. Somashekhar Maranoor  Senior Scale Lecturer, Science Department, Govt. Polytechnic, Bilagi, Karnataka, India
  • Mr. Umesh  Senior Scale Lecturer, Science Department, Govt. Polytechnic, Aurad(B), Karnataka, India

Keywords:

Abstract

We use in place of , and in place of when no ambiguity arises. Moreover, for , denotes the subgraph of induced by the vertices of . Similarly, for a vertex of , means . The connectivity of a connected graph is the least positive integer such that there exists , and is disconnected or reduces to the trivial graph . An obvious inference from the definition of is that for all . Consequently, (here stands for the degree and for the minimum degree). Also . Chang et.al., have proved Lemma 3.1.1.

References

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  2. C. D. Godsil, G. Royle, Algebraic Graph Theory, New York, (2001).
  3. J. A. Bondy and U. S. R. Murty, Graph Theory, Springer, (2008).
  4. G. J. Chang, L. Huang, X. Zhu, Circular chromatic number of Mycielski’s graph, Discrete Math., 205 (1999), 23 – 37.
  5. G. Chartrand and L. Lesniak, Graphs and Diagraphs, Chapman and Hall/CRC, America, (2000).
  6. M.E. Watkins, Connectivity of transitive graphs, J. Combin Theory, 8 (1970), 23 – 29.
  7. F. Harary, Graph Theory, Addison-Wesley, Reading, Mass, (1969).
  8. G. Chartrand and L. Lesniak, Graphs and Digraphs, Chapman and Hall/CRC, America, (2000).
  9. M.E. Watkins, Connectivity of transitive graphs, J. Combin Theory, 8

International Journal of Scientific Research in Science, Engineering and Technology

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Published

2021-01-25

Issue

Volume 8, Issue 1, January-February-2021

Section

Research Articles

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How to Cite

[1]
Mr. Somashekhar Maranoor, Mr. Umesh "Connectivity of The Mycielskian of A Graph" International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 8, Issue 1, pp.374-377, January-February-2021.