Let = (X,R) be a distance-regular graph of diameter d . A parallelogram of length i is a 4-tuple xyzw consisting of vertices of such that ∂(x, y)= ∂(z,w)= 1, ∂(x, z)= i, and ∂(x,w)= ∂(y,w)= ∂(y, z)= i− 1. A subset Y of X is said to be a completely regular code if the numbers πi,j = | j (x)∩ Y | (i, j ∈ {0,1, . . . , d}) depend only on i = ∂(x,Y ) and j . A subset Y of X is said to be strongly c...

The quest for a linear-time single-source shortest-path (SSSP) algorithm on directed graphs with positive edge weights is an ongoing hot research topic. While Thorup recently found an O(n +m) time RAM algorithm for undirected graphs with n nodes, m edges and integer edge weights in f0; : : : ; 2w 1g where w denotes the word length, the currently best time bound for directed sparse graphs on a R...

We study the class of simple graphs G for which every pair of distinct odd cycles intersect in at most one edge. We give a structural characterization of the graphs in G and prove that every G ∈ G satisfies the list-edge-coloring conjecture. When ∆(G) ≥ 4, we in fact prove a stronger result about kernel-perfect orientations in L(G) which implies that G is (m∆(G) : m)edge-choosable and ∆(G)-edge...

An extremely simple, linear time algorithm is given for constructing a domatic partition in totally balanced hypergraphs. This simpli es and generalizes previous algorithms for interval and strongly chordal graphs. On the other hand, the domatic number problem is shown to be NP-complete for several families of perfect graphs, including chordal and bipartite graphs.

In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks graphs of Steiner 2-designs, many Latin square graphs and strongly regular graphs whose intersection parameters are at most a quarter of their valency.

Large-scale distributed graph-parallel computing is challenging. On one hand, due to the irregular computation pattern and lack of locality, it is hard to express parallelism efficiently. On the other hand, due to the scale-free nature, realworld graphs are hard to partition in balance with low cut. To address these challenges, several graph-parallel frameworks including Pregel and GraphLab (Po...

Let H be a fixed graph on k vertices. For an edge-coloring c of H , we say that H is rainbow, or totally multicolored if c assigns distinct colors to all edges of H . We show, that it is easy to avoid rainbow induced graphs H . Specifically, we prove that for any graph H (with some notable exceptions), and for any graphs G, G 6= H , there is an edge-coloring of G with k colors which contains no...

The most common degradations in images is their poor contrast quality. Edge Enhancement is the art of examining images for identifying objects and judging their significance. The proposed paper uses the concept of hybrid edge detection method based on fuzzy sets and cellular learning automata to detect the gray level changes of neighbors of every pixel, and to detect the edge by using the chang...

Let G be a graph. A G-trade of volume m is a pair (T , T ′), where each of T and T ′ consists of m graphs, pairwise edge-disjoint, isomorphic to G, such that T ∩T ′ = ∅ and the union of the edge sets of the graphs in T is identical to the union of the edge sets of the graphs in T ′. Let X(G) be the set of non-negative integers m such that no G-trade of volume m exists. In this paper we prove th...