Circular Geodetic Number of Certain Graphs

Authors

  • Arul Amirtha Raja S Department of Mathematics, Loyola College, Chennai 600 034, India
  • Antony Xavier D Department of Mathematics, Loyola College, Chennai 600 034, India

Keywords:

Circular geodetic, Complete bipartite, Hexagonal mesh network, Apollonian

Abstract

A new variant geodetic problem, circular geodetic is defined as follows: Let S={x_1,x_2,...,x_k,x_(k+1)=x_1} be a geodetic set of G. Then S is said to be a circular geodetic set of G, there exists an index i, 1≤i≤k, such that I[x_i,x_(i+1)] contains atleast a vertex v other than x_i and x_(i+1), also I[S]=V(G). The minimum number of vertices needed to form a circular geodetic set is called circular geodetic number of G and it is denoted by g_cir (G).

References

[1] Jurczyk, M., Siegel, H. J., Stunkel, C. B., Interconnection Networks for Parallel Computers, Wiley Encyclopedia of Computer Science and Engineering, 2008.

[2] G.Chartrand, F. Harary, H. C. Swart and P. Zhang, Geodomination in Graphs, Bulletin of the ICA, 31(2001), 51-59.

[3] Pelayo, Ignacio M. Geodesic convexity in graphs. New York: Springer, 2013.

[4] G. Sabidussi, Graphs with given group and given graph-theoretical properties, Can. J. Math. 9 (1957) 515-525.

[5] Pelayo, Ignacio M. Geodesic convexity in graphs. New York: Springer, 2013.

[6] Hansberg, Adriana, and Lutz Volkmann. "On the geodetic and geodetic domination numbers of a graph." Discrete Mathematics 310.15 (2010): 2140-2146.

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Published

2025-11-25

How to Cite

[1]
S. Arul Amirtha Raja and D. Antony Xavier, “Circular Geodetic Number of Certain Graphs”, Int. J. Comp. Sci. Eng., vol. 7, no. 5, pp. 191–193, Nov. 2025.

Issue

Vol. 7 No. 5 (2019): IJCSE Special Issue Mar Edition

Section

Research Article

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