%0 Journal Article
%T Novel Properties of Fuzzy Labeling Graphs
%A A. Nagoor Gani
%A Muhammad Akram
%A D. Rajalaxmi (a) Subahashini
%J Journal of Mathematics
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/375135
%X The concepts of fuzzy labeling and fuzzy magic labeling graph are introduced. Fuzzy magic labeling for some graphs like path, cycle, and star graph is defined. It is proved that every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. We have shown that the removal of a fuzzy bridge from a fuzzy magic cycle with odd nodes reduces the strength of a fuzzy magic cycle. Some properties related to fuzzy bridge and fuzzy cut node have also been discussed. 1. Introduction Fuzzy set is a newly emerging mathematical framework to exemplify the phenomenon of uncertainty in real life tribulations. It was introduced by Zadeh in 1965, and the concepts were pioneered by various independent researches, namely, Rosenfeld [1] and Bhutani and Battou [2] during 1970s. Bhattacharya has established the connectivity concepts between fuzzy cut nodes and fuzzy bridges entitled ¡°Some remarks on fuzzy graphs [3].¡± Several fuzzy analogs of graph theoretic concepts such as paths, cycles, and connectedness were explored by them. There are many problems, which can be solved with the help of the fuzzy graphs. Though it is very young, it has been growing fast and has numerous applications in various fields. Further, research on fuzzy graphs has been witnessing an exponential growth, both within mathematics and in its applications in science and Technology. A fuzzy graph is the generalization of the crisp graph. Therefore it is natural that many properties are similar to crisp graph and also it deviates at many places. In crisp graph, a bijection that assigns to each vertex and/or edge if , a unique natural number is called a labeling. The concept of magic labeling in crisp graph was motivated by the notion of magic squares in number theory. The notion of magic graph was first introduced by Sunitha and Vijaya Kumar [4] in 1964. He defined a graph to be magic if it has an edge-labeling, within the range of real numbers, such that the sum of the labels around any vertex equals some constant, independent of the choice of vertex. This labeling has been studied by Stewart [5, 6] who called the labeling as super magic if the labels are consecutive integers, starting from 1. Several others have studied this labeling. Kotzig and Rosa [7] defined a magic labeling to be a total labeling in which the labels are the integers from 1 to . The sum of labels on an edge and its two endpoints is constant. Recently Enomoto et al. [8] introduced the name super edge magic for magic labeling in the sense of Kotzig and Rosa, with the added property that the vertices receive the smaller
%U http://www.hindawi.com/journals/jmath/2014/375135/