Shannon–Vizing–type problems concerning the upper bound for a distance chromatic index of multigraphs G in terms of the maximum degree ∆(G) are studied. Conjectures generalizing those related to the strong chromatic index are presented. The chromatic d–index and chromatic d–number of paths, cycles, trees and some hypercubes are determined. Among hypercubes, however, the exact order of their gro...

waveguides with low confinement loss, low chromatic dispersion, and low nonlinear effects are used in optical communication systems. optical fibers can also be employed in such systems. besides optical fibers, photonic crystal fibers are also highly suitable transmission media for optical communication systems. in this paper, we introduce two new designs of index-guiding photonic crystal fiber ...

The strong chromatic index of a graph is the minimum number of colours needed to colour the edges in such a way that each colour class is an induced matching. In this paper, we present bounds for the strong chromatic index of three different products of graphs in terms of the strong chromatic index of each factor. For the Cartesian product of paths, cycles or complete graphs, we derive sharper ...

The star chromatic index χs(G) of a graph G is the minimum number of colors needed to properly color the edges of the graph so that no path or cycle of length four is bi-colored. We obtain a near-linear upper bound in terms of the maximum degree ∆ = ∆(G). Our best lower bound on χs in terms of ∆ is 2∆(1 + o(1)) valid for complete graphs. We also consider the special case of cubic graphs, for wh...

Waveguides with low confinement loss, low chromatic dispersion, and low nonlinear effects are used in optical communication systems. Optical fibers can also be employed in such systems. Besides optical fibers, photonic crystal fibers are also highly suitable transmission media for optical communication systems. In this paper, we introduce two new designs of index-guiding photonic crystal fiber ...

In his Master’s thesis, Ján Mazák proved that the circular chromatic index of the type 1 generalized Blanuša snark B n equals 3+ 2 n . This result provided the first infinite set of values of the circular chromatic index of snarks. In this paper we show the type 2 generalized Blanuša snark B n has circular chromatic index 3 + 1 b1+3n/2c . In particular, this proves that all numbers 3 + 1/n with...

We prove that the circular chromatic index of a cubic graph G with 2k vertices and chromatic index 4 is at least 3 + 2/k. This bound is (asymptotically) optimal for an infinite class of cubic graphs containing bridges. We also show that the constant 2 in the above bound can be increased for graphs with larger girth or higher connectivity. In particular, if G has girth at least 5, its circular c...