Incidence cuts and connectivity in fuzzy incidence graphs

Document Type: Original Manuscript

Authors

1 Assistant Professor, Department of Mathematics, NIT Calicut

2 Creighton University

3 Shaanxi Normal University China

Abstract

Fuzzy incidence graphs can be used as models for nondeterministic interconnection networks having extra node-edge
relationships. For example, ramps in a highway system may be modeled as a fuzzy incidence graph so that unexpected
flow between cities and highways can be effectively studied and controlled. Like node and edge connectivity in graphs,
node connectivity and arc connectivity in fuzzy incidence graphs are introduced in this article. Their relationships with
fuzzy connectivity parameters are discussed and results similar to Whitney’s theorems are obtained. Also, the incidence
is used to model flows in human trafficking networks.


Keywords


[1] M. Akram, W. A. Dudek, Intuitionistic fuzzy hypergraphs with applications , Information Sciences, 218 (2013), 182-193.
[2] M. Akram, W. A. Dudek,
Regular bipolar fuzzy graphs , Neural Computing and Applications, 1 (2011), 1-9.
[3] M. Akram, Neha Waseem, Wieslaw A. Dudek,
Certain types of edge m-polar fuzzy graphs, Iranian Journal of fuzzy systems, 14(4) (2017), 27-50.
[4] K. R. Bhutani, A. Rosenfeld,
Geodesics in fuzzy graphs, Electronic Notes in Discrete Mathematics, 15 (2013), 51-54.
[5] K. R. Bhutani, A. Rosenfeld,
Strong arcs in fuzzy graphs, Information Sciences, 152 (2003), 19-322.
[6] T. Dinesh,
A study on graph structures, incidence algebras and their fuzzy analogues, Ph. D. Thesis, Kannur University,
Kerala, India, 2012.
[7] T. Dinesh,
Fuzzy incidence graph-an introduction, Advances in Fuzzy Sets and Systems, 21(1) (2016), 33-48.
[8] S. Mathew, J. N. Mordeson, 
Connectivity concepts in fuzzy incidence graphs, Information Sciences, 382(383) (2017), 326-333.
[9] S. Mathew, J. N. Mordeson, Davender S Malik,
Fuzzy Graph Theory, Springer, New York, 2018.
[10] S. Mathew, M. S. Sunitha,
Strongest strong cycles and θ-fuzzy graphs, IEEE Transactions on Fuzzy Systems, 21(6) (2013), 1096-1104.
[11] S. Mathew, M. S. Sunitha,
Types of arcs in a fuzzy graph, Information Sciences, 179(11) (2009), 1760-1768.
[12] J. N. Mordeson,
Fuzzy incidence graphs, Advances in Fuzzy Sets and Systems, 21(2) (2016), 1-13.
[13] J. N. Mordeson, P. S. Nair,
Fuzzy Graphs and Fuzzy Hypergraphs, New York, Physica-Verlag, Heidelberg, Germany, 2000.
[14] J. N. Mordeson, P. S. Nair,
Fuzzy Mathematics, Physica-Verlag, Heidelberg, Germany, 2001.
[15] J. N. Mordeson, S. Mathew,
Fuzzy endnodes in fuzzy incidence graphs, New Mathematics and Natural Computation, Special issue: Human Trafficking, 13(3) (2017), 13-20.
[16] J. N. Mordeson, S. Mathew,
Human trafficking: Source, transit, destination, designations, New Mathematics and Natural Computation, Special issue: Human Trafficking, 13(3) (2017), 209-218.
[17] J. N. Mordeson, S. Mathew,
Local look at human trafficking, New Mathematics and Natural Computation, Special issue: Human Trafficking, 13(3) (2017), 327-340.
[18] J. N. Mordeson, S. Mathew, D. Malik, Fuzzy Graph Theory with Applications to Human trafficking, Springer 2018.
[19] A. Rosenfeld,
Fuzzy Graphs, In: L. A. Zadeh, K. S. Fu, and M. Shimura (Eds.), Fuzzy Sets and their Applications, Academic Press, 1975, 77-95.
[20] M. Sarwar, M. Akram,
Novel applications of m-polar fuzzy concept lattice, New Mathematics and Natural Computation, 13(3) (2017), 196-222.
[21] M. S. Sunitha, A. Vijayakumar,
A characterization of fuzzy trees, Information Sciences, 113 (1999), 293-300.
[22] M. S. Sunitha, A. Vijayakumar,
Blocks in fuzzy graphs, The Journal of Fuzzy Mathematics, 13(1) (2005), 13-23.
[23]
Trafficking in Persons: Global Patterns, Appendices-United Nations Office on Drugs and Crime, Citation Index, pp. 54-102, 2006.
[24] R. T. Yeh, S. Y. Bang,
Fuzzy relations, fuzzy graphs and their applications to clustering analysis, In: L. A. Zadeh, K. S. Fu and M. Shimura (Eds.), Fuzzy Sets and Their Applications, Academic Press, 1975, 125-149.
[25] L. A. Zadeh,
Fuzzy sets, Information and Control, 8 (1965), 338-353.