On the traversability of near common neighborhood graph of a graph

Authors

  • Keerthi G Mirajkar Department of Mathematics, Karnatak University's, Karnatak Arts College, Dharwad.
  • Anuradha V Deshpande Karnatak University's, Karnatak Arts College, Dharwad.

DOI:

https://doi.org/10.23755/rm.v41i0.626

Keywords:

Near common neighborhood graph, Hamiltonian graph, Eulerian graph

Abstract

The near common neighborhood graph of a graph G, denoted by
ncn(G) is defined as the graph on the same vertices of G, two vertices
are adjacent in ncn(G), if there is at least one vertex in G not adjacent
to both the vertices. In this research paper, the conditions for ncn(G)
to be disconnected are discussed and also we present characterization
for graph ncn(G) to be hamiltonian and eulerian.

References

A.N Al-Kenani, A. Alwardi, and O.A. Al-Attas. On the near-common neighborhood graph of a graph. International Journal of Computer Applications, 146(1), 2016.

F. Harary. Graph Theory. Addison-Wesley Mass, Reading, New York, 1969.

G.S. Singh. Graph Theory. PHI Learning Private Limited, New York, 2010.

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Published

2021-12-31

Issue

Vol. 41 (2021)

Section

Volume 41-2021

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