A study on strong arcs in fuzzy graphs and union of fuzzy graphs∗

C Y Ponnappan; A Selvam

doi:10.48165/

Authors

C Y Ponnappan Research Supervisor and Assistant Professor of Mathematics, Government Arts College, Melur, Tamilnadu -625106, India.
A Selvam Lecturer in Mathematics, B.C.M. Government Women’s Polytechnic College, Ettayapuram, Tamilnadu, India.

DOI:

https://doi.org/10.48165/

Keywords:

Fuzzy graph, Strong n the union of fuzzy graphs, Some basic theorems and resuarc, Domination number, Effective edge domination, Strong arc domination number

Abstract

In the present work, we discuss the union operation and strong arc domina tion on fuzzy graphs. We determine the bounds for the strong arc domination number of fuzzy graphs. Further, this new dominationFuzzy graph parameter is discussed ilts are obtained in the union of fuzzy graphs.

References

V[1] Zadeh, L.A. (1965). Fuzzy sets, Information and Control, 8, 338 – 353.

Ore, O. (1962). Theory of Graphs, Amer. Math. Soc. Colloq., Publication 38, Providence, U.S.A. [3] Monderson, N. John and Nair, S. Premchand (2000). Fuzzy Graphs and Fuzzy Hypergraphs, Physica Verlag, New York.

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

Rosenfeld, A. (1975). Fuzzy graphs, in Zadeh, L.A., Fu, K.S. and Shimura,M. (Editors), Fuzzy Sets and Their Applications, Academic Press, New York.

Harary, F. (1969). Graph Theory, Addison Wesley, Reading, MA.

Nagoorgani, A. and Chandrasekaran, V.T (2006). Domination in fuzzy graph, Advances In Fuzzy Sets and Systems, 1(1), 17–26.

Bhutani, K.R. and Rosenfeld, A. (2003). Storng arcs in fuzzy graph, Information Sciences, 152, 319–322.

Bhutani, K.R., Mordeson, J. and Rosenfeld, A. (2004). On degrees of end node and cut node in fuzzy graphs, Iranian Journal of Fuzzy Systems, 1(1), 57–64.

Strong arcs in fuzzy graphs ... 675

Debnath, Pradip (2013). Domination in interval valued fuzzy graphs, Ann.Fuzzy Math. Inform., 6(2) , 363–370.

Yeh, R.T., Bang, S.Y. (1975). Fuzzy relations, fuzzy graphs and their applications to clustering analysis, in Zadeh, L.A., Fu, K.S. and Shimura, M. (Editors), Fuzzy Sets and Their Applications to Cognitive and Decision Processes, Academic Press, New York, 125–149.

Cockayne, E.J. and Hedetnieme, S.T. (1977). Towards a theory of domination in graphs, Networks, 7, 247–261.