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 edges in every other color class. We give in this work bounds for the b-chromatic index of the direct product of graphs and provide general results for many direct products of regular graphs. In addition, we introduce a l...

A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b-chromatic number b(G) of a graph G is the largest integer k such that G admits a b-coloring with k colors. A simple graph G is called b-vertex (edge) critical if the removal of any vertex (edge) of G increases its b-chromatic number. In thi...

We measured the responses of 305 neurons in striate cortex to moving sinusoidal gratings modulated in chromaticity and luminance about a fixed white point. Stimuli were represented in a 3-dimensional color space defined by 2 chromatic axes and a third along which luminance varied. With rare exceptions the chromatic properties of cortical neurons were well described by a linear model in which th...

Let G $G$ be a simple graph with maximum degree Δ ( ) ${\rm{\Delta }}(G)$ and chromatic index χ ′ $\chi ^{\prime} (G)$ . A classical result of Vizing shows that either = (G)={\rm{\Delta or + 1 }}(G)+1$ is called edge- }}$ -critical if connected, − e (G-e)={\rm{\Delta for every ∈ E $e\in E(G)$ an n $n$ -vertex graph. conjectured α $\alpha , the independence number at most 2 $\frac{n}{2}$ The cur...

for a graph $g$ with edge set $e(g)$, the multiplicative sum zagreb index of $g$ is defined as$pi^*(g)=pi_{uvin e(g)}[d_g(u)+d_g(v)]$, where $d_g(v)$ is the degree of vertex $v$ in $g$.in this paper, we first introduce some graph transformations that decreasethis index. in application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum zagreb ...

This paper investigates into the added value of color information for edge extraction and straight edge segment matching between stereo views. For edge extraction in color images different methods proposed in the literature are evaluated and compared, paying special attention to significance and completeness of the obtained edge-map. To find related edge segment pairs in different views, we app...