On fz- Domination Number of Fuzzy Graphs

A Lekha, K.S Parvathy

Abstract


Given a fuzzy graph G = (V; ; ), the fz- domination number, fz(G),
is the least scalar cardinality of an fz- dominating set of G. In this article,
we examine several features of fz-domination number of fuzzy
graphs as a result of various fuzzy graph operations. We find bounds
for the fz-domination number of a few graph products and look at the
requirements for the sharpness of these bounds.


Keywords


fuzzy graph; fz-dominating sets; fz-domination number; graph operations

Full Text:

PDF

References


S. A. K. Bhutani and L. Sathikala. On (r,s)-fuzzy domination in fuzzy graphs.

New Mathematics and Natural Computation 12(01):1-10, 2016.

N. Gani and V. Chandrasekaran. Domination in fuzzy graph. Advances in Fuzzy

Sets and Systems, 1, 01 2006.

E. C. G. S. Hedetniemi and C. Mynhardt. Properties of minimal dominating functions

of graphs. Technical Report, DMS-547-IR, 1990.

S. H. S. Hedetniemi and T. Wimer. Linear time resourse allocation algorithms

for trees. Technical Report URL-014, Department of Mathematics, Clemson

University, 1987.

A. Lekha and K. S. Parvathy. Fuzzy domination in fuzzy graphs. Journal of

Intelligent and Fuzzy Systems, 2022. doi: 10.3233/JIFS-220987.

O. T. Manjusha and M. S. Sunitha. Strong domination in fuzzy graphs. Fuzzy

Information and Engineering, 7(3):369-377, 2015.

J. N. Mordeson and P. Chang-Shyh. Operations on fuzzy graphs. Information

Sciences, 79(3):159–170, 1994. ISSN 0020-0255.

J. N. Mordeson and P. S. Nair. Fuzzy Graphs and Fuzzy Hypergraphs. Physica-

Verlag, 2000.

A. Rosenfeld. Fuzzy graphs. In Fuzzy Sets and their Applications to Cognitive

and Decision Processes, pages 77–95. Academic Press, 1975.

A. Somasundaram. Domination in products of fuzzy graphs. International Journal

of Uncertainty, Fuzziness and Knowledge-Based Systems Vol. 13, No. 2

(2005) 195-204, World Scientific Publishing Company, 2005.

A. Somasundaram and S. Somasundaram. Domination in fuzzy graphs – i. Pattern

Recognition Letters, 19(9):787–791, 1998. ISSN 0167-8655.




DOI: http://dx.doi.org/10.23755/rm.v46i0.1078

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 A Lekha, K.S Parvathy

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

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.