For an edge-colored graph G , we call edge–cut M of monochromatic if the edges are colored with same color. The is called monochromatically disconnected any two distinct vertices separated by a edge–cut. connected disconnection number denoted m d ( ) maximum colors that needed in order to make disconnected. We show almost all graphs have numbers equal 1. also obtain Nordhaus–Gaddum-type results...

This paper presents an alternative approach to the image segmentation problem. Similar to other recent proposals a graph theoretic framework is used: Given an image a weighted undirected graph is constructed, where each pixel becomes a vertex of the graph and edges measure a relationship between pixels. Our approach differs from previous work in the way we define the edge weights. Typically the...

A circuit cover of an edge-weighted graph (G, p) is a multiset of circuits in G such that every edge e is contained in exactly p(e) circuits in the multiset. A nonnegative integer valued weight vector p is admissible if the total weight of any edge-cut is even, and no edge has more than half the total weight of any edge-cut containing it. A graph G has the circuit cover property if (G, p) has a...

Given an undirected unweighted graph G = (V, E) and an integer k ≥ 1, we consider the problem of computing the edge connectivities of all those (s, t) vertex pairs, whose edge connectivity is at most k. We present an algorithm with expected running time Õ(m + nk) for this problem, where |V | = n and |E| = m. Our output is a weighted tree T whose nodes are the sets V1, V2, . . . , V` of a partit...

forest roads are directions in natural habitats that used to transport wood products, secondary forest products and recreation. constructing forest roads causes trees clearing with specified width thus lead to direct or indirect changes in forest ecosystems and forest environment. this study aims to assess the changes of diversity and richness indices in main and secondary forest roads in a par...

For a connected graph G = (V, E), an edge set S ⊆ E is a k-restricted edge cut if G−S is disconnected and every component of G− S has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum k-restricted edge cut. Let ξk(G) = min{|[X, X ]| : |X | = k,G[X ] is connected}. G is λk -optimal if λk(G) = ξk(G). Moreover, G is super-λk ...

A vertex-cut X is said to be a restricted cut of a graph G if it is a vertex-cut such that no vertex u in G has all its neighbors in X. Clearly, each connected component of G − X must have at least two vertices. The restricted connectivity κ′(G) of a connected graph G is defined as the minimum cardinality of a restricted cut. Additionally, if the deletion of a minimum restricted cut isolates on...

In this paper, the concept of hypergraph is extended to the fuzzy hypergraph. In the fuzzy hypergraph, the concepts of a-cut hypergraph, strength of edge and dual fuzzy hypergraph are developed. It is shown that the fuzzy hypergraph and a-cut hypergraph are useful to represent a fuzzy partition. An application example also shows that the strength of edge can be used to decompose the data set in...