Vague Graphs Research Articles

Some properties of vague graphs with application

Theoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. The vague graphs are more flexible and compatible than fuzzy graphs due to the fact that they have many applications in networks. In this paper, busy vertices, free vertices, strong arc, busy value, isolated vertex, fully free vertex and partial free vertex in vague graphs are defined. Likewise, some interesting properties of isomorphism and weak isomorphism on them are introduced. Finally, we give an application of vague digraph in vulnerability assessment of gas pipeline networks.

Isomorphic properties of neighborly irregular vague graphs

The main purpose of this paper is to introduce weak isomorphism, co-weak isomorphism and isomorphism of neighborly irregular vague graphs. Some results on order, size and degree of nodes in isomorphic neighborly irregular and isomorphic highly irregular vague graphs are discussed. Isomorphism between neighborly irregular and highly irregular vague graphs are proved to be an equivalence relation. Density and balanced irregular vague graphs are introduced. Finally, an application of vague graphs is given.

Vague graphs and strengths

Vague graphs and strengths

Semi global domination sets in vague graphs with application

Semi global domination sets in vague graphs with application

New concepts of vague graphs

The concept of vague graph was introduced by Ramakrishna (Int J Comput Cognit 7:51–58, 2009). Since the vague models give more precision, flexibility, and compatibility to the system as compared to the classical and fuzzy models, in this paper, the concept of energy of fuzzy graph is extended to the energy of a vague graph. It has many applications in physics, chemistry, computer science, and other branches of mathematics. We define adjacency matrix, degree matrix, laplacian matrix, spectrum, and energy of a vague graph in terms of their adjacency matrix. The spectrum of a vague graph appears in physics statistical problems, and combinatorial optimization problems in mathematics. Also, the lower and upper bounds for the energy of a vague graph are also derived. Finally, we give some applications of energy in vague graph and other sciences.

Product vague graphs and its applications

Product vague graphs and its applications

DEGREE OF VERTICES IN VAGUE GRAPHS

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G1 and G2 using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

Domination in vague graphs and its applications

The concept of vague graph introduced by Ramakrishna in [8]. The main purpose of this paper is to introduce the concepts of cardinality, dominating set, independent set, total dominating number and independent dominating number of a vague graph. The notion of irredundance number of a vague graph is discussed, too. Finally we give an application of domination in vague graphs.

Certain types of vague cycles and vague trees

Fuzzy models are becoming useful because of their aim of reducing the differences between the traditional numerical models used in engineering and sciences and the symbolic models used in expert systems. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduce various types of vague bridges, vague cut-vertices, vague cycles and vague trees in vague graphs, and investigate some of their interesting properties. Most of these various types are defined in terms of levels. We also describe comparison of these types.

Regularity in Vague Intersection Graphs and Vague Line Graphs

Fuzzy graph theory is commonly used in computer science applications, particularly in database theory, data mining, neural networks, expert systems, cluster analysis, control theory, and image capturing. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduce the notion of vague line graphs, and certain types of vague line graphs and present some of their properties. We also discuss an example application of vague digraphs.

Some Operations on Vague Graphs

Some Operations on Vague Graphs