The main purpose of this paper is to introduce the notion of vague h-morphism on vague graphs and regular vague graphs. The action of vague h-morphism on vague strong regular graphs are studied. Some elegant results on weak and co weak isomorphism are derived. Also, [Formula: see text]-complement of highly irregular vague graphs are defined.

In this paper we prove that any distance-balanced graph $G$ with $Delta(G)geq |V(G)|-3$ is regular. Also we define notion of distance-balanced closure of a graph and we find distance-balanced closures of trees $T$ with $Delta(T)geq |V(T)|-3$.

Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.

Algorithms that nd good partitionings of highly unstructured graphs are critical in developing eÆcient algorithms for problems in a variety of domains such as scienti c simulations that require solution to large sparse linear systems, VLSI design, and data mining. Even though this problem is NP-hard, eÆcient multi-level algorithms have been developed that can nd good partitionings of static irr...

The isomorphism classes of several types of graph coverings of a graph have been enumerated by many authors [M. Hofmeister, Graph covering projections arising from finite vector space over finite fields, Discrete Math. 143 (1995) 87–97; S. Hong, J.H. Kwak, J. Lee, Regular graph coverings whose covering transformation groups have the isomorphism extention property, Discrete Math. 148 (1996) 85–1...

The concept of vague graph was introduced by Ramakrishna in [12]. 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. The main purpose of this paper is to introduce the concept of dominating set, perfect dominating set, minimal perfect dominating set and i...

let g be a graph. the first zagreb m1(g) of graph g is defined as: m1(g) = uv(g) deg(u)2. in this paper, we prove that each even number except 4 and 8 is a first zagreb index of a caterpillar. also, we show that the fist zagreb index cannot be an odd number. moreover, we obtain the fist zagreb index of some graph operations.