Doubly connected geodetic number of graphs

K.L. Bhavyavenu; Venkanagouda M. Goudar

doi:10.26637/MJM0603/0025

Abstract

In this paper, we investigate the results on doubly connected geodetic number of a simple graph $G$, shadow distance graph and corona of two graphs. Further we verify how doubly connected geodetic number is affected by adding a pendant vertex.

Keywords:

Corona, Geodetic number, shadow distance graphs, Vertex covering number

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

K.L. Bhavyavenu Research Scholar, Sri Siddhartha Academy of Higher Education, Tumkur-572107, Karnataka, India.
Venkanagouda M. Goudar Sri Siddhartha Academy of Higher Education, Department of Mathematics, Sri Siddhartha Institute of Technology, Tumkur-572105, Karnataka, India. https://orcid.org/0000-0002-9738-4236

Pages: 626-631
Date Published: 01-07-2018
Vol. 6 No. 03 (2018): Malaya Journal of Matematik (MJM)

K.L. Bhavyavenu and Venkanagouda M. Goudar, Doubly connected geodetic number on operations in Graphs, Journal of Engineering and Applied Sciences, 13(7)(2018), 4330-4335.

G. Chartrand, F. Harary and P. Zhang, On the geodetic number of a graph, Networks, 39(1)(2002), 1-6.

G. Chartrand and P. Zhang, Introduction to Graph Theory , Tata Mc-Graw Hill Pub. Co. Ltd, 2006.

F. Harary, Graph theory, Addition-Weseley, 1969.

A.P. Santhakumaran, P.Titus and J.John, On the connected geodetic number of a graph, Journal of Combinatorial Mathematics and Combinatorial Computing, 69(2009), 219-229.

K.M. Tejaswini and Venkanagouda M. Goudar, Non split geodetic number of a graph, International Journal of Mathematical Combinatorics, 2(2016), 109-120.

Venkanagouda M. Goudar, K.M. Tejaswini and Venkatesha, Strong Non-split geodetic number of a graph, $I n-$ ternational Journal of Computer Application, 5(2014), 171-183.

Venkanagouda M. Goudar, K.S. Ashalatha and Venkatesh, Split geodetic number of a graph" Advances and Applications in Discrete Mathematics, 13(1)(2014), 9-22.

U. Vijaya Chandra Kumar and R. Muruli, Edge domination in the shadow distance graph of some star related graphs, Annals of Pure and Applied Mathematics, 13(1)(2017), 33-40.

D.B.West, Introduction to Graph Theory, 2nd edition, Prentice Hall, USA, 2001.