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.

Submit Article

SIGNED HUB SETS IN SIGNED GRAPHS

Authors

  • K. S. Shama
  • T. V. Ramakrishnan
  • P. M. Divya

Keywords:

signed graph, signed hub set, signed hub number

DOI:

https://doi.org/10.17654/0974165826008

Abstract

In this paper, we introduce and investigate the concept of signed hub sets in signed graphs. A signed graph is a graph where each edge is labeled either positive or negative. Extending the notion of hub sets from unsigned graphs, we define a signed hub set in a signed graph as a subset of vertices ensuring that every pair of non-hub vertices is either directly connected by a positive edge or through a positive path whose internal vertices are all from the signed hub set. We define the signed hub number as the minimum cardinality of such a hub set and establish several foundational results.

Received: July 27, 2025
Revised: November 23, 2025
Accepted: December 9, 2025

References

[1] Matthew Walsh, The hub number of a graph, Int. J. Math. Comput. Sci. 1 (2006), 117-124.

[2] E. C. Cuaresma Jr. and R. N. Paluga, On the hub number of some graphs, Annals of Studies in Science and Humanities 1(1) (2015), 17-24.

[3] G. Chartrand and P. Zang, Introduction to Graph Theory, Tata McGraw-Hill, 2009.

[4] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, The Macmillan Press Ltd., 1976.

[5] F. Harary, Graph Theory, Addison-Wesley, Reading, Massachusetts, 1972.

[6] F. Harary, On the notion of balance of a signed graph, Michigan Math. J. 2 (1953), 143-146.

[7] T. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, 1998.

[8] T. Zaslavsky, Signed graphs, Discrete Appl. Math. 4 (1982), 47-74.

[9] B. D. Acharya, Domination and absorbance in signed graphs and digraphs: I. Foundations, J. Combin. Math. Combin. Comput. 84 (2013), 5-20.

[10] K. A. Germina and P. Ashraf, On open domination and domination in signed graphs, Int. Math. Forum 8 (2013), 1863-1872.

[11] A. J. Mathias, V. Sangeetha and M. Acharya, Restrained domination in signed graphs, Acta Univ. Sapientiae Math. 12 (2020), 155-163.

[12] O. Ore, Theory of graphs, American Mathematical Society Colloquium Publications, American Mathematical Society, Providence, RI, 1962.

[13] H. B. Walikar, S. V. Motammanavar and B. D. Acharya, Signed domination in signed graph, J. Comb. Inf. Syst. Sci. 40 (2015), 107-128.

[14] P. Jeyalakshmi, Domination in signed graphs, Discrete Math. Algorithms Appl. 13 (2021), Paper No. 2050094, 11 pp.

[15] T. Zaslavsky, A mathematical bibliography of signed and gain graphs and allied areas, Electron. J. Combin. 5 (1998), Dynamic Surveys 8, 124 pp.

Downloads

Published

2026-01-02

Issue

Vol. 43 No. 1 (2026)

Section

Articles

License

Copyright (c) 2026 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

_________________________

Licensing Terms:

Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.

Contact Pushpa Publishing House for more info or permissions.

How to Cite

SIGNED HUB SETS IN SIGNED GRAPHS. (2026). Advances and Applications in Discrete Mathematics, 43(1), 119-135. https://doi.org/10.17654/0974165826008

Similar Articles

1-10 of 177

You may also start an advanced similarity search for this article.