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The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex adjacent to some vertex in all the other color classes. It is proved that with four exceptions, the b-chromatic number of cubic graphs is 4. The exceptions are the Petersen graph, K 3,3 , the prism over… (More)

The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex that has a neighbor in each of the other color classes. We prove that every d-regular graph with at least 2d 3 vertices has b-chromatic number d + 1, that the b-chromatic number of an arbitrary d-regular… (More)

Vertex-colorings, edge-colorings and total-colorings of the Sierpi´nski gasket

The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex that has a neighbor in each of the other color classes. We prove that every d-regular graph with at least 2d 3 vertices has b-chromatic number d + 1, that the b-chromatic number of an arbitrary d-regular… (More)

- Marko Jakovac, Iztok Peterin
- 2011

A b-coloring is a proper vertex coloring 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 is the largest integer ϕ(G) for which a graph has a b-coloring with ϕ(G) colors. We determine some upper and lower bounds for the b-chromatic number of the strong product G H, the… (More)

- Marko Jakovac
- 2009

Graphs S[n, k] are introduced as the graphs obtained from the Sierpi´nski graphs S(n, k) by contracting edges that lie in no triangle. The family S[n, k] is a previously studied class of Sierpi´nski gasket graphs S n. Several properties of graphs S[n, k] are studied in particular, hamiltonicity and chromatic number.

Bite force is the condition, expression and measure of the masticatory function. The purpose of this study was to examine, by means of a newly constructed electronic gnathodynamometer, the values of maximal bite forces in subjects with complete dentition, the time in which they express 50% and 75% respectively of the total forces value, and the shape of the… (More)

A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by ψ k (G) the minimum cardinality of a k-path vertex cover in G. In this paper improved lower and upper bounds for ψ k of the Cartesian and the direct product of paths are derived. It is shown that for ψ 3 those… (More)

OBJECTIVES
The purpose of this research was to determine the mass concentrations of ions eluted from dental ceramic after an exposure to hydrochloric acid and, drawing on those results, to develop a feedforward backpropagation neural network (NN).
MATERIALS AND METHODS
Four dental ceramics were selected for this study. The experimental measurement was… (More)