A graph X is max-λ if λ(X) = δ(X). A graph X is super-λ if X is max-λ and every minimum edge-cut set of X isolates one vertex. In this paper, we proved that for all but a few exceptions, the mixed Cayley graph which is defined as a new kind of semi-regular graph is max-λ and super-λ. c © 2008 Elsevier B.V. All rights reserved.

A 4-restricted edge cut is an edge cut of a connected graph which disconnects the graph, where each component has order at least 4. Graphs that contain 4-restricted edge cuts are characterized in this paper. As a result, it is proved that a connected graph G of order at least 10 contains 4-restricted edge cuts if and only if it contains no cut-vertex u where every component of G \ u has order a...

A cubic graph G is uniquely edge-3-colorable if G has precisely one 1-factorization. It is proved in this paper, if a uniquely edge-3-colorable, cubic graph G is cyclically 4-edgeconnected, but not cyclically 5-edge-connected, then G must contain a snark as a minor. This is an approach to a conjecture that every triangle free uniquely edge-3-colorable cubic graph must have the Petersen graph as...

Given an undirected edge-weighted graph, G = (V,E), the maximum cut problem (Max-Cut) is to find a bipartition of the vertices that maximizes the weight of the edges crossing the partition. If the edge weights are non-negative, then this problem is equivalent to finding a maximum weight subset of the edges that forms a bipartite subgraph, i.e. the maximum bipartite subgraph problem. All results...

Das, Basanta Kumar, Ji GanG Kim, and Ji Weon Choi, 2011. edge browning and microbial quality of fresh-cut iceberg lettuce with different sanitizers and contact times. Bulg. J. Agric. Sci., 17: 55-62 This study was conducted to evaluate the effect of different washing solutions and contact times on the cut edge browning and microbial quality of fresh-cut iceberg lettuce. samples were cut into sm...

Let G be a connected graph with minimum degree δ and edgeconnectivity λ. A graph is maximally edge-connected if λ = δ, and it is superedge-connected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. In this paper, we show that a connected graph or a connected triangle-free graph is maximally edge-connected or sup...

Let G = (V, E) be a connected graph. Let G = (V, E) be a connected graph. An edge set F ⊂ E is said to be a k-restricted edge cut, if G− F is disconnected and every component of G− F has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is the cardinality of a minimum k-restricted edge cut of G. A graph G is λk-connected, if G contains a k-restricted edge cut. A λk...

A fullerene graph is a planar cubic graph whose all faces are pentagonal and hexagonal. The structure of cyclic edge-cuts of fullerene graphs of sizes up to 6 is known. In the paper we study cyclic 7-edge connectivity of fullerene graphs, distinguishing between degenerated and non-degenerated cyclic edge-cuts, regarding the arrangement of the 12 pentagons. We prove that if there exists a non-de...

In this paper, a new algorithm for edge detection based on fuzzyconcept is suggested. The proposed approach defines dynamic membershipfunctions for different groups of pixels in a 3 by 3 neighborhood of the centralpixel. Then, fuzzy distance and -cut theory are applied to detect the edgemap by following a simple heuristic thresholding rule to produce a thin edgeimage. A large number of experime...