Issue 3 Volume 6 (2018)

Regular Issue Special Issue
Authors : P. Anitha
Title : Vizing's Weaker Conjecture $(\delta,\Delta) = (7,15)$
Volume, Issue, Year : 6(3)(Special Issue)(2018)
Pages : 1−8

Abstract: Vizing conjectured that $G$ is a simple and $\Delta$-critical graph with $m$ edges then $2m \geq \Delta^2$. In this paper, we prove, the conjecture for graphs with $\delta = 7$ and $\Delta = 15$.

Keywords: Critical graphs, degree sequence.

Authors : R. Queen Mary and D. Selvi
Title : Solving Fuzzy Assignment Problem Using Centroid Ranking Method
Volume, Issue, Year : 6(3)(Special Issue)(2018)
Pages : 9−16

Abstract: Assignment problem has various applications in the real world because of their wide applicability in industry, commerce, management science, etc. Traditional classical assignment problems cannot be successfully used for real life problem; hence the use of fuzzy assignment problem is more appropriate. Fuzzy sets were introduced by Lofti A. Zadeh in 1965 as an extension of representing impreciseness or vagueness in day to day life. In this paper, Triangular Fuzzy Assignment Problem has been defuzzified into crisp values using Centroid Ranking method and Hungarian method has been applied to find an optimal solution.The proposed method is illustrated by numerical examples.

Keywords: Fuzzy Assignment Problem, Triangular Fuzzy Number, Triangular Fuzzy Assignment Problem, Centroid Ranking Method.

Authors : G. Meena and K. Nagarajan
Title : Wheel Related Intersection Cordial Labeling of Graphs
Volume, Issue, Year : 6(3)(Special Issue)(2018)
Pages : 17−21

Abstract: An intersection cordial labeling of a graph G with vertex set $V$ is an injection $f$ from $V$ to the power set of $\{1, 2,\dots , n \}$ such that if each edge $uv$ is assigned the label $1$ if $f(u)\cap f(v)\neq \emptyset $ and 0 otherwise; Then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has an intersection cordial labeling, then it is called intersection cordial graph. In this paper, we proved the wheel related graphs are intersection cordial.

Keywords: Cordial labeling, Intersection cordial labeling, Intersection cordial graphs.

Authors : S. Vimala
Title : Q(a) Balance Edge-Magic of Few Connected Graphs
Volume, Issue, Year : 6(3)(Special Issue)(2018)
Pages : 23−26

Abstract: In this paper Q(a)-BEM label is discussed the following connected graphs such as Cycle graph, Ladder graph and Gear graph. If G is a $(p,q)$- graph in which the edges are labeled $1,2,3,\dots,q$ so that the vertex sums are constant mod p, then G is called an Edge-Magic graph (in short, EM graph). Our purpose of this work is to show that in Q(a)-BEM graphs.

Keywords: Edge magic, balance edge-magic graph, Q(a) balance edge-magic graph, Cycle graph, Ladder graph, Gear graph.

Authors : S. P. Kanniga Devi and K. Nagarajan
Title : Divisor Degree Index of Graphs
Volume, Issue, Year : 6(3)(Special Issue)(2018)
Pages : 27−30

Abstract: In this paper, we introduce the concepts of divisor degree of a vertex v and divisor degree index dd (G) of a simple graph G. We also introduce maximum divisor degree and minimum divisor degree of a simple graph G. Also, we find divisor degree of some standard graphs and establish the relation between degree and divisor degree index of graphs.

Keywords: Degree, Divisor degree index, Maximum divisor degree and Minimum divisor degree.

Authors : P. Veerammal and G. Velammal
Title : L-Fuzzy Almost Subgroups
Volume, Issue, Year : 6(3)(Special Issue)(2018)
Pages : 31−36

Abstract: Algebraic structures like fuzzy sub groups of L-Fuzzy sets have been well studied in the case where the lattice L is distributive. By slightly relaxing the relevant axioms the concepts can be generalised to the case where the lattice is not distributive. The aim of this current paper is to define the concept of L-Fuzzy Almost Subgroup (LFASG) and investigate some of its properties.

Keywords: L-Fuzzy Sets, L-Fuzzy subgroup, L-Fuzzy Almost subgroup, Non-Distributive lattice, Almost level set.

Authors : A.Ponselvakumari and R.Selvi
Title : Some Results in Fuzzy Soft $\beta$-Continuity
Volume, Issue, Year : 6(3)(Special Issue)(2018)
Pages : 37−44

Abstract: $\beta$-continuous functions, fuzzy $\beta $-continuous functions and soft $\beta$-continuous functions have been already investigated by topologists. In this paper the concept of a fuzzy soft $\beta $-continuous function is introduced and its relationship with the existing concept in the literature of fuzzy soft topology is discussed.

Keywords: Fuzzy soft sets, Fuzzy soft topology, Fuzzy soft mapping, Fuzzy soft $\beta $-continuous.