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Circular Geodetic Number of Certain Graphs

S. Arul Amirtha Raja1 , D. Antony Xavier2

Section:Research Paper, Product Type: Journal Paper
Volume-07 , Issue-05 , Page no. 191-193, Mar-2019

CrossRef-DOI:   https://doi.org/10.26438/ijcse/v7si5.191193

Online published on Mar 10, 2019

Copyright © S. Arul Amirtha Raja, D. Antony Xavier . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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IEEE Style Citation: S. Arul Amirtha Raja, D. Antony Xavier, “Circular Geodetic Number of Certain Graphs,” International Journal of Computer Sciences and Engineering, Vol.07, Issue.05, pp.191-193, 2019.

MLA Style Citation: S. Arul Amirtha Raja, D. Antony Xavier "Circular Geodetic Number of Certain Graphs." International Journal of Computer Sciences and Engineering 07.05 (2019): 191-193.

APA Style Citation: S. Arul Amirtha Raja, D. Antony Xavier, (2019). Circular Geodetic Number of Certain Graphs. International Journal of Computer Sciences and Engineering, 07(05), 191-193.

BibTex Style Citation:
@article{Raja_2019,
author = {S. Arul Amirtha Raja, D. Antony Xavier},
title = {Circular Geodetic Number of Certain Graphs},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {3 2019},
volume = {07},
Issue = {05},
month = {3},
year = {2019},
issn = {2347-2693},
pages = {191-193},
url = {https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=830},
doi = {https://doi.org/10.26438/ijcse/v7i5.191193}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v7i5.191193}
UR - https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=830
TI - Circular Geodetic Number of Certain Graphs
T2 - International Journal of Computer Sciences and Engineering
AU - S. Arul Amirtha Raja, D. Antony Xavier
PY - 2019
DA - 2019/03/10
PB - IJCSE, Indore, INDIA
SP - 191-193
IS - 05
VL - 07
SN - 2347-2693
ER -

           

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).

Key-Words / Index Term

Circular geodetic, Complete bipartite, Hexagonal mesh network, Apollonian

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.