On Geodesic Convexity in Mycielskian of Graphs

S. Gajavalli; A. Berin Greeni

doi:10.20965/jaciii.2023.p0119

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JACIII Vol.27 No.1 pp. 119-123

doi: 10.20965/jaciii.2023.p0119

(2023)

Research Paper:

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On Geodesic Convexity in Mycielskian of Graphs

S. Gajavalli and A. Berin Greeni

School of Advanced Sciences, Vellore Institute of Technology
Vandalur, Kelambakkam Road, Chennai 600127, India

Received:

June 30, 2022

Accepted:

November 16, 2022

Published:

January 20, 2023

Keywords:

convexity number, geodetic number, geodetic iteration number, hull number, Mycielskian of a graph

Abstract

The convexity induced by the geodesics in a graph G is called the geodesic convexity of G. Mycielski graphs preserve the property of being triangle-free and many parameters such as power domination number, coloring number, determining number and recently general position number have been determined for them. In this work, we determine the geodesic convexity parameters viz., convexity, geodetic iteration, geodetic, and hull numbers for Mycielski graphs for which the underlying graphs considered are path, cycle, star, and complete graph.

Cite this article as:

S. Gajavalli and A. Greeni, “On Geodesic Convexity in Mycielskian of Graphs,” J. Adv. Comput. Intell. Intell. Inform., Vol.27 No.1, pp. 119-123, 2023.

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References

[1] F. Harary and J. Nieminen, “Convexity in graphs,” J. Differ. Geom., Vol.16, pp. 185-190, 1981.
[2] G. Chartrand, C. E. Wall, and P. Zhang, “The Convexity Number of a Graph,” Graphs Comb., Vol.18, pp. 209-17, 2002.
[3] F. Harary, E. Loukakis, and C. Tsouros, “The geodetic number of a graph,” Math. Comput. Modelling, Vol.17, No.11, pp. 89-95, 1993.
[4] M. Atici, “Computational Complexity of Geodetic Set,” Int. J. Comput. Math., Vol.79, No.5, pp. 587-591, 2002.
[5] M. G. Everett and S. B. Seidman, “The hull number of a graph,” Discrete Math., Vol.57, No.3, pp. 217-223, 1985.
[6] B. Bresar, T. K. Šumenjak, and A. Tepeh, “The geodetic number of the lexicographic product of graphs,” Discrete Math., Vol.311, No.16, pp. 1693-1698, 2011.
[7] J. Caceres, C. Hernando, M. Mora, I. M. Pelayo, and M. L. Puertas, “On the geodetic and the hull numbers in strong product graphs,” Comput. Math. with Appl., Vol.60, No.11, pp. 3020-3031, 2010.
[8] G. Chartrand, J. F. Fink, and P. Zhang, “Convexity in oriented graphs,” Discret. Appl. Math., Vol.116, No.2, pp. 115-126, 2002.
[9] F. Buckley and F. Harary, “Distance in graphs,” Addison Wesley Publishing Company, 1990.
[10] I. M. Pelayo, “Geodesic convexity in graphs,” Springer, 2013.
[11] H. P. Patil and R. P. Raj, “On the total graph of Mycielski graphs, central graphs and their covering numbers,” Discuss. Math. Graph Theory, Vol.33, pp. 361-371, 2013.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] F. Harary and J. Nieminen, “Convexity in graphs,” J. Differ. Geom., Vol.16, pp. 185-190, 1981.

[2] [2] G. Chartrand, C. E. Wall, and P. Zhang, “The Convexity Number of a Graph,” Graphs Comb., Vol.18, pp. 209-17, 2002.

[3] [3] F. Harary, E. Loukakis, and C. Tsouros, “The geodetic number of a graph,” Math. Comput. Modelling, Vol.17, No.11, pp. 89-95, 1993.

[4] [4] M. Atici, “Computational Complexity of Geodetic Set,” Int. J. Comput. Math., Vol.79, No.5, pp. 587-591, 2002.

[5] [5] M. G. Everett and S. B. Seidman, “The hull number of a graph,” Discrete Math., Vol.57, No.3, pp. 217-223, 1985.

[6] [6] B. Bresar, T. K. Šumenjak, and A. Tepeh, “The geodetic number of the lexicographic product of graphs,” Discrete Math., Vol.311, No.16, pp. 1693-1698, 2011.

[7] [7] J. Caceres, C. Hernando, M. Mora, I. M. Pelayo, and M. L. Puertas, “On the geodetic and the hull numbers in strong product graphs,” Comput. Math. with Appl., Vol.60, No.11, pp. 3020-3031, 2010.

[8] [8] G. Chartrand, J. F. Fink, and P. Zhang, “Convexity in oriented graphs,” Discret. Appl. Math., Vol.116, No.2, pp. 115-126, 2002.

[9] [9] F. Buckley and F. Harary, “Distance in graphs,” Addison Wesley Publishing Company, 1990.

[10] [10] I. M. Pelayo, “Geodesic convexity in graphs,” Springer, 2013.

[11] [11] H. P. Patil and R. P. Raj, “On the total graph of Mycielski graphs, central graphs and their covering numbers,” Discuss. Math. Graph Theory, Vol.33, pp. 361-371, 2013.