Abstract. Let #tex2html_wrap_inline20# be a fuzzy graph. Let #tex2html_wrap_inline22# and #tex2html_wrap_inline24# be two vertices of #tex2html_wrap_inline26#. A subset #tex2html_wrap_inline28# of #tex2html_wrap_inline30# is called a fuzzy equitable dominating set if every #tex2html_wrap_inline32# there exist a vertex #tex2html_wrap_inline34# such that#tex2html_wrap_inline36# and #math12##tex2html_wrap_inline38# where #tex2html_wrap_inline40# denotes the degree of vertex #tex2html_wrap_inline42# and #tex2html_wrap_inline44# denotes the degree of vertex #tex2html_wrap_inline46# and #math13##tex2html_wrap_inline48#. The minimum cardinality of a fuzzy equitable dominating set is denoted by #tex2html_wrap_inline50#. In this paper we introduce the concept of fuzzy equitable dominating set, minimal fuzzy equitable dominating set, strong (weak) fuzzy equitable dominating set , fuzzy equitable independent set and obtain some interesting results for this new parameter in equitable fuzzy graphs.

Received: February 10, 2014

AMS Subject Classification: 05C72

Key Words and Phrases: fuzzy equitable dominating set, fuzzy equitable neighborhood, fuzzy equitable independent set

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DOI: 10.12732/ijpam.v94i5.3 rawhtml6#

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 94
Issue: 5
Pages: 661 -- 667

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DOI (International DOI Foundation); WorldCAT.

This work is licensed under the Creative Commons Attribution International License (CC BY).

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