The Ordered Binary Decision Diagram (OBDD) has been efficiently used to compute the communication network (CN) reliability (REL). The boundary set method (BS) is used to improve the efficiency of the OBDD approach, while the augmented OBDD diagrams (OBDD-A) that stores CN information in its nodes has been proposed to solve other CN performance metrics in addition to REL. The hybrid OBDD (OBDD-H...

The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...

For c ∈ [0, 1] let Pn(c) denote the set of n-vertex perfect graphs with density c and Cn(c) the set of n-vertex graphs without induced C5 and with density c. We show that log2 |Pn(c)|/ (

Cographs are exactly the hereditarily well-colored graphs, i.e., graphs for which a greedy vertex coloring of every induced subgraph uses only minimally necessary number colors χ(G). Greedy colorings shown to be subclass hierarchical that naturally appear in phylogenetic combinatorics. The cographs form special class minimal colorings. fact cotrees modular decomposition trees suggests natural g...

Single crystals of octa-deca-nickel dodeca-germanide were grown by chemical transport reaction. The inter-metallic compound crystallizes in a superstructure of the hexa-gonal NiAs type (B8 type). All atoms in the asymmetric unit lie on special positions except one Ni atom (two Ni atoms have site symmetry -6.. and another one has site symmetry .2. while the Ge atoms have site symmetries 32., m.....

A vertex cover of a hypergraph is set vertices which intersects each hyperedge. possesses property C(k,ρ) iff |⋂E′|<ρ for k element E′ hyperedges. Komjáth proved that every uniform possessing C(2,r) some r∈ω has minimal cover. In this paper we will relax the assumption uniformity to an cardinalities hyperedges “small” infinite cardinals, e.g. it countable, or does not contain uncountably many l...

An anti-magic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the integers {1, ..., q} such that all p vertex sums are pairwise distinct, where the vertex sum on a vertex is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it has an anti-magic labeling. Hartsfield and Ringel [3] conjectured t...

The crossing number of a graph G, cr(G), is defined as the smallest possible edge-crossings in drawing G plane. There are almost no results concerning join disconnected 6-vertex with cycle. main aim this paper to give product Q+Cn for Q consisting two 3-cycles, where Cn cycle on n vertices.