A dominating set D of an IFG G = (V, E) is a non-split dominating set, if the induced intuitionistic fuzzy subgraph 〈ܸ − ‫〉ܦ‬ is connected. The Non-split domination number ߛ ௡௦ ሺ‫ܩ‬ሻ of IFG G is the minimum cardinality of all Non-split dominating set. In this paper we study some theorems in Non-split dominating sets of IFG and some results of ߛ ௡௦ ሺ‫ܩ‬ሻwith other known parameters of IFG G. 1. In...

A path P connecting a pair of vertices in connected fuzzy graph is called detour, if its μ - length maximum among all the feasible paths between them. In this paper we establish notion detour convex sets, covering, basis, number, blocks and investigate some their properties. It has been proved that, for complete G, set any G covering. necessary sufficient condition to become block also establis...

The Fuzzy logic concept is implemented in several image processing operations such as edge detection, segmentation, object recognition, etc. In this paper, a novel Image encryption algorithm based on multiple fuzzy graph (FG) mapping technique is proposed. The Fuzzy graphs are obtained from a matrix of size n and then they are used to encrypt an image. Here fuzzy graphs with triangular and sigm...

Connectivity has an important role in neural networks, computer network, and clustering. In the design of a network, it is important to analyze connections by the levels. The structural properties of intuitionistic fuzzy graphs provide a tool that allows for the solution of operations research problems. In this paper, we introduce various types of intuitionistic fuzzy bridges, intuitionistic fu...

In this paper we introduce the concept of strong total domination in fuzzy graphs. We determine the strong total domination number for several classes of fuzzy graphs. A lower bound and an upper bound for the strong total domination number in terms of strong domination number is obtained. Strong total domination in fuzzy trees is studied. A necessary and sufficient condition for the set of fuzz...

Since categories are graphs with additional “structure”, one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility degree that determines to what extend it is possible to “go” from one object to another one. These categories are called fuzzy categories. Of course, the basic p...

In this thesis we focus our attention on the stable set polytope of claw-free graphs. This problem has been open for many years and albeit all the efforts engaged during those last three years, it is still open. This does not mean that no progress has been made and we hope to the contrary that this thesis contains some important advances and that the reader will share this point of view. Unders...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...