For any graph G, let V (G) and E(G) denote the vertex set and the edge set of G respectively. The Boolean function graph B(G, L(G), NINC) of G is a graph with vertex set V (G) ∪ E(G) and two vertices in B(G, L(G), NINC) are adjacent if and only if they correspond to two adjacent vertices of G, two adjacent edges of G or to a vertex and an edge not incident to it in G. For brevity, this graph is denoted by B1(G). In this paper, we determine domination number, independent, connected, total, point-set, restrained, split and non-split domination numbers in the complement B1(G) of B1(G) and obtain bounds for the above numbers.
The eccentricity e(v) of a vertex v is the distance from v to a vertex farthest from v, and u is an eccentric vertex for v if its distance from v is d(u, v) = e(v). A vertex of maximum eccentricity in a graph G is called peripheral, and the set of all such vertices is the peripherian, denoted PeriG). We use Cep(G) to denote the set of eccentric vertices of vertices in C(G). A graph G is called an S-graph if Cep(G) = Peri(G). In this paper we characterize S-graphs with diameters less or equal to four, give some constructions of • S-graphs and investigate S-graphs with one central vertex. We also correct and generalize some results of F. Gliviak.
The article explains why it is necessary to deal with a mechanical stress in thin film coatings especially in multilayer systems. The published model’s properties are overviewed and a new alternative model of mechanical stress in multilayer is proposed. Both models are compared including the discussion of their advantages for utilization in different situations. and V článku jsou uvedeny důvody, proč je významné se zabývat mechanickým napětím tenkých vrstev, zejména systémem více vrstev. Shrnuje vlastnosti modelu uvedeného v literatuře a podává odvození alternativního popisu jednotlivých vrstev. Jsou porovnány oba přístupy a uvedeny výhody jejich použití v různých případech.