Open Access   Article Go Back

On the Doubly Edge Geodetic Number of a Graph

D. Antony Xavier1 , Elizabeth Thomas2

Section:Research Paper, Product Type: Journal Paper
Volume-07 , Issue-05 , Page no. 208-212, Mar-2019

CrossRef-DOI:   https://doi.org/10.26438/ijcse/v7si5.208212

Online published on Mar 10, 2019

Copyright © D. Antony Xavier, Elizabeth Thomas . 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.

View this paper at   Google Scholar | DPI Digital Library

XML View
PDF Download

How to Cite this Paper

  • IEEE Citation
  • MLA Citation
  • APA Citation
  • BibTex Citation
  • RIS Citation

IEEE Style Citation: D. Antony Xavier, Elizabeth Thomas, “On the Doubly Edge Geodetic Number of a Graph,” International Journal of Computer Sciences and Engineering, Vol.07, Issue.05, pp.208-212, 2019.

MLA Style Citation: D. Antony Xavier, Elizabeth Thomas "On the Doubly Edge Geodetic Number of a Graph." International Journal of Computer Sciences and Engineering 07.05 (2019): 208-212.

APA Style Citation: D. Antony Xavier, Elizabeth Thomas, (2019). On the Doubly Edge Geodetic Number of a Graph. International Journal of Computer Sciences and Engineering, 07(05), 208-212.

BibTex Style Citation:
@article{Xavier_2019,
author = {D. Antony Xavier, Elizabeth Thomas},
title = {On the Doubly Edge Geodetic Number of a Graph},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {3 2019},
volume = {07},
Issue = {05},
month = {3},
year = {2019},
issn = {2347-2693},
pages = {208-212},
url = {https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=834},
doi = {https://doi.org/10.26438/ijcse/v7i5.208212}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v7i5.208212}
UR - https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=834
TI - On the Doubly Edge Geodetic Number of a Graph
T2 - International Journal of Computer Sciences and Engineering
AU - D. Antony Xavier, Elizabeth Thomas
PY - 2019
DA - 2019/03/10
PB - IJCSE, Indore, INDIA
SP - 208-212
IS - 05
VL - 07
SN - 2347-2693
ER -

           

Abstract

Geodetic number and its variants is one of the widely studied topic in the field of graph theory. Over the recent years many variants of geodetic number have been extensively studied in the literature. In this paper, we introduce a new variation called doubly edge geodetic number and proved that it is Np-complete. The doubly edge geodetic number for some standard graphs is determined. Furthermore, certain characterization and realization results of doubly edge geodetic number are discussed.

Key-Words / Index Term

doubly edge geodetic set, doubly geodetic set, geodesic, geodetic set

References

[1] Buckley F., Harary F., Distance in Graphs(Addison- Wesley, Redwood City, CA, 1990).R. Solanki, “Principle of Data Mining”, McGraw-Hill Publication, India, pp. 386-398, 1998.
[2] Harary F., Graph Theory (Reading, MA: Addison-Wesley,1969).
[3] Atici M., On the edge geodetic number of a graph, International Journal of Computer Mathematics, 80, 2003,853-861
[4] Santhakumaran A. P., and John J., Edge geodetic number of a graph, J. Discrete Math. Sci.Cryptography, 10(3), 2007,415-432.
[5] Santhakumaran A. P., and Jebaraj T., Double geodetic number of a graph, DiscussionesMathematicae Graph Theory 32(1), 2012, 109-119.
[6] Chartrand G., Harary F., and Zhang P., On the geodetic number of a graph,Networks, 39(1), 2002, 1-6.