The automorphic A-chromatic index of a graph Γ is the minimum integer m for which Γ has a proper edge-coloring with m colors which is preserved by a given subgroup A of the full automorphism group of Γ. We compute the automorphic A-chromatic index of each generalized Petersen graph when A is the full automorphism group.

Let L # Kp be a p-chromatic graph and e be are edge of I, such that L e is (p IL)chromatic. If Cn is a graph of n vertices without contain&g L but containing Kp, then the minimum valence of Gn is

It is proved that every graph embedded in a fixed surface with sufficiently large edge-width is acyclically 7-colorable and that its star chromatic number is at most 2s * 0 + 3, where s * 0 ≤ 20 is the maximum star chromatic number for the class of all planar graphs.

Chromatic induction from a surrounding light is measured with an additional remote field outside the surround. Chromatic induction from the surround into a central test field is found to be attenuated by a remote inhomogeneous 'checkerboard', composed of squares at two different chromaticities. A uniform remote field, on the other hand, either at the average or at the most extreme chromaticity ...

An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label $f^+(x)= \sum f(e)$, with $e$ ranging over all edges incident $x$. The chromatic number $G$, denoted by $\chi_{la}(G)$, minimum distinct labels labelings $G$. In this...

PURPOSE To measure in vivo and objectively the monochromatic aberrations at different wavelengths, and the chromatic difference of focus between green and infrared wavelengths in eyes implanted with two models of intraocular lenses (IOL). METHODS EIGHTEEN EYES PARTICIPATED IN THIS STUDY: nine implanted with Tecnis ZB99 1-Piece acrylic IOL and nine implanted with AcrySof SN60WF IOL. A custom-d...

A simple graph-product type construction shows that for all natural numbers r ≥ q, there exists an edge-coloring of the complete graph on 2 vertices using r colors where the graph consisting of the union of arbitrary q color classes has chromatic number 2. We show that for each fixed natural number q, if there exists an edge-coloring of the complete graph on n vertices using r colors where the ...

A proper edge colouring of a graph is said to be acyclic if every cycle of G receives at least three colors. The acyclic chromatic index, denoted , is the least number of colors required for an acyclic edge color of . This paper shows an upper bound of the acyclic chromatic index of a class of graphs which can be expressed as the Cartesian product of some graphs. We also give exact values for s...