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)
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)
Vertex-colorings, edge-colorings and total-colorings of the Sierpi´nski gasket
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 complete subgraph K k. The family S[n, k] is a generalization of a previously studied class of Sierpi´nski gasket graphs Sn. Several properties of graphs S[n, k] are studied in particular, hamiltonicity and chromatic number.
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)
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 article a lower and an upper bound for ψ k of the rooted product graphs are presented. Two characterizations are given when those bounds are… (More)
Dental ceramics represents a major structural material in fixed prosthodontics. Increasing demands for esthetics led to development of new ceramic materials in order to eliminate the use of metal framework and for all ceramic restorations with mechanical properties to withstand high occlusal forces. Out of all the present ceramic materials,… (More)