TARU PUBLICATIONS
Journal of Information and Optimization Sciences cover

Journal of Information and Optimization Sciences

(Since 1980)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

Powered by:Powered by

Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

Issues up to 2022 co-published with and available at:Taylor & Francis
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Information and Optimization Sciences
Open Access Research Article

Some results on the open subset intersection graph of a product topological space

, , * ,

* Corresponding author · click or hover a name for details

pp. 697–707Vol. 44Issue 4May 2023DOI: 10.47974/JIOS-1229XML
Received:
02 Feb 2022
Accepted:
02 Jul 2022
Published Online:
28 Aug 2023
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1229
Pages:
697–707

Abstract

In the recent paper, R. A. Muneshwar et al., introduced a graph structure called open subset intersection graph g(t)  on a topological space (X, t).  In this paper, we study some important results of a graph g(t)  of a product topological space (X × Y, t).  We also determine relationship between diameter, girth, clique number, chromatic number, domination number etc. of an open subset intersection graph of a topological space (X × Y, t), (X, tX) and  (Y, tY). Moreover, we proved that, if (X, tX)  and (Y, tY)  are discrete topological space then w(g(tX × tY)) = w(g(tX)) * w(g(tY)) – 2 and c(g(tX × tY)) = c(g(tX)) * c(g(tY)) – 2  and domination number of g(tX × tY)  is 2. We also determine diameter and girth of intersection Graph of Product Topology on X × Y  for different values of m and n.

Keywords

Discrete topologyGraphDiameterGirthClique numberChromatic numberDomination numberDegree

Subject Classifications

05C2505C6905C0705C12

References

[1] D. F. Anderson and P. S. Livingston: The zero-divisor graph of a commutative ring, Journal of Algebra, 217 (1999), 434-447 .
[2] I. Beck: Coloring of commutative rings, Journal of Algebra, 116(1), (1988), 208-226 .
[3] I. Chakrabarty, S. Ghosh, T.K. Mukherjee and M.K. Sen: Intersection graphs of ideals of rings, Discrete Mathematics 309, 17 (2009): 5381-5392.
[4] A. Das: Non-Zero Component Graph of a Finite Dimensional Vector Space, Communications in Algebra, Vol. 44, Issue 9, 2016: 3918-3926.
[5] A. Das: Subspace Inclusion Graph of a Vector Space, Communications in Algebra, Vol. 44, Issue 11, 2016: 4724-4731.
[6] A. Das: Non-Zero Component Graph of a Finite Dimensional Vector Space, Commu-nications in Algebra, to appear. available at http://arxiv.org/abs/1506.04905.
[7] N. Jafari Rad, S.H. Jafari: Results on the intersection graphs of subspaces of a vector space, http://arxiv.org/abs/1105.0803v1.
[8] R. A. Muneshwar, K. L. Bondar, Open Subset Inclusion Graph of a Topological Space. Journal of Discrete Mathematical Sciences and Cryptography, Vol.-22, Issue-6, 2019, pp.-1007-1018.
[9] R. A. Muneshwar, K. L. Bondar, Some Significant Properties of the Intersection Graph Derived from Topological Space Using Intersection of Open Sets, Far East Journal of Mathematical Sciences (FJMS), Vol.-119, Issue-1, 2019, pp.-29-48.
[10] R. A. Muneshwar, K. L. Bondar, Some Properties of the Union Graph Derived from Topological Space Using Union of Open Sets. Far East Journal of Mathematical Sciences (FJMS), Vol.-121, Issue-2, 2019, pp.-101-121.
[11] R. A. Muneshwar, K. L. Bondar, Some properties of open subset intersection graph of a topological space, Journal of Information and Optimization Sciences, Val.-42, Isuue - 5, pp.-1129-1136, DOI: 10.1080/02522667.2021.1877902.(2021). 
[12] R. A. Muneshwar, K. L. Bondar, Some results on an intersection graph of a topology, Journal of Discrete Mathematical Sciences and Cryptography, Vol. - 24, Issue - 4, pp. - 1053-1062, DOI: 10.1080/09720529.2021.1877408, (2021) 
[13] Y. Talebi, M.S. Esmaeilifar, S. Azizpour: A kind of intersection graph of vector space, Journal of Discrete Mathematical Sciences and Cryptography 12, no. 6, 681-689, 2009.
[14] Wasadikar, M., Survase, P.: Incomparability Graphs of Lattices. In: Balasubramaniam, P., Uthayakumar, R. (eds.) ICMMSC 2012. CCIS, vol. 283, pp. 78-85. Springer, Heidelberg (2012).
[15] D.B. West: Introduction to Graph Theory, Prentice Hall, 2001.
[16] Robert B. Allan and Renu Laskar, On domination and independent domination number of a graph, Discrete Math. 23 (1978), 73-76.
[17] D. B. West, Introduction to Graph Theory, Prentice Hall, 2001. 
[18] Narsingh Deo, Graph Theory with Application to Engineering and Computer Science, PHI Learning Private Limited, 2012.
[19] M. Wasadikar and P. Survase, Incomparability graphs of lattices, International Conference on Mathematical Modelling and Scientific Computation (ICMMSC) 2012: Mathematical Modelling and Scientific Computation, Communications in Computer and Information Science Book Series (CCIS), Springer, Heidelberg, Volume 283, 2012, pp. 78-85. 

Views: 158Downloads: 66Citations: 0