Some Aspects of Radial Graphs Under Boolean Operations

Authors

  • S. Vetriselvi Department of Mathematics, Mepco Schlenk Engineering College (affiliated to the Anna University), Sivakasi, Virudhunagar 626005, Tamilnadu, India https://orcid.org/0000-0001-6989-9438
  • G. Sangeetha Centre for Research and Post Graduate Studies in Mathematics, Ayya Nadar Janaki Ammal College (affiliated to Madurai Kamaraj University), Sivakasi 626124, Virudhunagar, Tamilnadu, India https://orcid.org/0009-0006-1488-1314

DOI:

https://doi.org/10.26713/cma.v15i1.2122

Keywords:

Radial graph, Conjunction, Rejection, Cartesian product

Abstract

Two vertices of a graph \(G\) are said to be radial to each other if the distance between them is equal to the radius of the graph. The radial graph of a graph \(G\), denoted by \(R(G)\), has the vertex set as in \(G\) and two vertices are adjacent in \(R(G)\) if and only if they are radial to each other in \(G\). If \(G\) is disconnected, then the two vertices are adjacent in \(R(G)\) if they belong to different components of \(G\). The main objective of this paper is to determine the radial graphs of some families of product graphs.

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References

G. Abay-Asmerom, R. Hammack, C. E. Larson and D. T. Taylor, Notes on the independence number in the Cartesian product of graphs, Discussiones Mathematicae Graph Theory 31(1) (2011), 25 – 35, URL: https://eudml.org/doc/270895.

J. Akiyama, K. Ando and D. Avis, Eccentric graphs, Discrete Mathematics 56(1) (1985), 1 – 6, DOI: 10.1016/0012-365X(85)90188-8.

S. Avadayappan and M. Bhuvaneswari, A note on radial graphs, Journal of Modern Science 7 (1)(2015), 14 – 21.

E. M. El-Kholy, El-Said R. Lashin and S. N. Daoud, New operations on graphs and graph foldings, International Mathematical Forum 7(46) (2012), 2253 – 2268.

F. Harary, Graph Theory, Addison-Wesley Publishing Company, Reading, ix + 274 pages (1969).

F. Harary and G. W. Wilcox, Boolean operations on graphs, Mathematica Scandinavica 20 (1967), 41 – 51, DOI: 10.7146/math.scand.a-10817.

K. M. Kathiresan and G. Marimuthu, A study on radial graphs, Ars Combinatoria 96 (2010), 353 – 360, URL: http://combinatoire.ca/ArsCombinatoria/Vol96.html.

K. Kathiresan and G. Marimuthu, Further results on radial graphs, Discussiones Mathematicae Graph Theory 30(1) (2010), 75 – 83, DOI: 10.7151/dmgt.1477.

P. M. Weichsel, The Kronecker product of graphs, Proceedings of the American Mathematical Society 13 (1962), 47 – 52, DOI: 10.1090/S0002-9939-1962-0133816-6.

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Published

24-04-2024
CITATION

How to Cite

Vetriselvi, S., & Sangeetha, G. (2024). Some Aspects of Radial Graphs Under Boolean Operations. Communications in Mathematics and Applications, 15(1), 185–190. https://doi.org/10.26713/cma.v15i1.2122

Issue

Vol. 15 No. 1 (2024)

Section

Research Article

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