THE COMPLETE PRODUCT OF TWO FUZZY GRAPHS AND ITS RELATIONSHIP WITH FUZZY GRAPH ISOMORPHISM

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 27

Abstract

Fuzzy graph was introduced by Kaufmann [7] in 1973. In this paper, we introduced the concept of the complete product of two fuzzy graphs with an Illustrative example. We proved the result that If $G:(\sigma,\mu)=(U,E_U)$, $H:(\tau,\vartheta)=(V,E_V)$, $G':(\sigma',\mu')=(U',E_{U'})$ and $H':(\tau',\vartheta')=(V',E_{V'})$ are any four fuzzy graphs such that $G:(\sigma,\mu)\cong G':(\sigma',\mu')$ and $H:(\tau,\vartheta)\cong H':(\tau',\vartheta')$ under the fuzzy graph isomorphisms $f$ and $h$ respectively, then $G\times_PH\cong G'\times_P H'$. As the proof is too long, we have demonstrated the result in two by parting into two hypotheses.

Keywords and Phrases

Fuzzy relation, Fuzzy graph, Uniform vertex fuzzy graph, Fuzzy graph isomorphism, The complete product of two fuzzy graphs.

A.M.S. subject classification

05C70, 05C72.

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