Advances and Applications in Discrete Mathematics

The Advances and Applications in Discrete Mathematics is a prestigious peer-reviewed journal indexed in the Emerging Sources Citation Index (ESCI). It is dedicated to publishing original research articles in the field of discrete mathematics and combinatorics, including topics such as graphs, coding theory, and block design. The journal emphasizes efficient and powerful tools for real-world applications and welcomes expository articles that highlight current developments in the field.

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THE ECCENTRIC HUB NUMBER OF A GRAPH

Authors

  • Veena Mathad
  • Parvathi

Keywords:

hub number, eccentric hub number, eccentric hub graph.

DOI:

https://doi.org/10.17654/0974165823062

Abstract

A set $H \subseteq V(G)$ is eccentric hub set of a graph $G$ if $H$ is a hub set of $G$ and also every $v \in V(G) \backslash H$ has an eccentric vertex in $H$. The minimal eccentric hub set with minimum cardinality is called minimum eccentric hub set. Its cardinality is eccentric hub number of $G$, denoted by $e h(G)$. In this paper, we deduce some results and bounds on this parameter. Further, we have studied about total number of minimum eccentric hub sets and eccentric hub graphs.

Received: June 14, 2023;
Accepted: August 2, 2023

References

F. Harary, Graph Theory, Addison Wesley, Reading Mass, 1969.

T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker Inc., 1998.

T. N. Janakiraman, M. Bhanumathi and S. Muthammai, Eccentric domination in graphs, International Journal of Engineering Science Advanced Computing and Bio-Technology 1(2) (2010), 55-70.

Matthew Walsh, The hub number of a graph, International Journal of Mathematics and Computer Science 1 (2006), 117-124.

Shadi Ibrahim Khalaf, Veena Mathad and Sultan Senan Mahde, Hubtic number in graphs, Opuscula Mathematica 38(6) (2018), 841-847.

Shadi Ibrahim Khalaf, Veena Mathad and Sultan Senan Mahde, Hub and global hub numbers of a graph, Proceedings of the Jangjeon Mathematical Society 23(2) (2020), 231-239.

Tracy Grauman, Stephen G. Hartke, Adam Jobson, Bill Kinnersley, Douglas B. West, Lesley Wiglesworth, Pratik Worah and Hehui Wu, The hub number of a graph, Information Processing Letters 108 (2008), 226-228.

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Published

2023-09-15

Issue

Vol. 40 No. 2 (2023)

Section

Articles

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How to Cite

THE ECCENTRIC HUB NUMBER OF A GRAPH. (2023). Advances and Applications in Discrete Mathematics, 40(2), 139-165. https://doi.org/10.17654/0974165823062

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