We have developed a technique for color image enhancement based on a model of the Human Visual System HVS A color image represented by RGB is rst transformed into a color space based on the HVS cone response characteristics Subsequently chromatic correlation reduction and energy compression is realized by using a multispectral Karhunen Lo eve transform KLT of the cone responses This yields a co...

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...

We show that the 2-edge-colored chromatic number of a class of simple graphs is bounded if and only if the acyclic chromatic number is bounded for this class. Recently, the CSP dichotomy conjecture has been reduced to the case of 2-edge-colored homomorphism and to the case of 2-vertex-colored homomorphism. Both reductions are rather long and follow the reduction to the case of oriented homomorp...

Following [1], we investigate the problem of covering a graph G with induced subgraphs G1, . . . , Gk of possibly smaller chromatic number, but such that for every vertex u of G, the sum of reciproquals of the chromatic numbers of the Gi’s containing u is at least 1. The existence of such “chromatic coverings” provides some bounds on the chromatic number of G.

A strong edge-coloring of a graph G is a function that assigns to each edge a color such that two edges within distance two apart must receive different colors. The minimum number of colors used in a strong edge-coloring is the strong chromatic index of G. Lih and Liu [14] proved that the strong chromatic index of a cubic Halin graph, other than two special graphs, is 6 or 7. It remains an open...

Let R be a commutative ring with $Z(R)$ its set of zero-divisors. In this paper, we study the total graph of $R$, denoted by $T(Gamma(R))$. It is the (undirected) graph with all elements of R as vertices, and for distinct $x, yin R$, the vertices $x$ and $y$ are adjacent if and only if $x + yinZ(R)$. We study the chromatic number and edge connectivity of this graph.

I must have known Dirac when he was a child in the 1930's, but I really became aware of his existence when I visited England for the first time after the war in February and March 1949 . We met in London and he told me of his work on chromatic graphs . Dirac defined a k-chromatic graph to be vertex critical if the omission of any vertex decreases the chromatic number and edge critical if the re...

The b-chromatic index φ(G) of a graph G is the largest integer k such that G admits a proper k-edge coloring in which every color class contains at least one edge incident to some edge in all the other color classes. The b-chromatic index of trees is determined and equals either to a natural upper bound m(T ) or one less, where m(T ) is connected with the number of edges of high degree. Some co...

A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studi...

the vertex-edge wiener index of a simple connected graph g is defined as the sum of distances between vertices and edges of g. two possible distances d_1(u,e|g) and d_2(u,e|g) between a vertex u and an edge e of g were considered in the literature and according to them, the corresponding vertex-edge wiener indices w_{ve_1}(g) and w_{ve_2}(g) were introduced. in this paper, we present exact form...