In communication networks, the binding numbers of graphs (or networks) are often used to measure vulnerability and robustness networks). Furthermore, fractional factors ID-[a, b]-factor-critical covered have a great deal important applications in data transmission networks. this paper, we investigate relationship between graphs, derive number condition for graph be covered, which is an extensio...

Graph mining and management has become an important topic of research recently because of numerous applications to a wide variety of data mining problems in computational biology, chemical data analysis, drug discovery and communication networking. Traditional data mining and management algorithms such as clustering, classification, frequent pattern mining and indexing have now been extended to...

Graph mining and management has become an important topic of research re-cently because of numerous applications to a wide variety of data mining prob-lems in computational biology, chemical data analysis, drug discovery and com-munication networking. Traditional data mining and management algorithmssuch as clustering, classification, frequent pattern mining and indexing have no...

Graph mining and management has become an important topic of research recently because of numerous applications to a wide variety of data mining problems in computational biology, chemical data analysis, drug discovery and communication networking. Traditional data mining and management algorithms such as clustering, classification, frequent pattern mining and indexing have now been extended to...

A graph G is well-covered provided each maximal independent set of vertices has the same cardinality. The term sk of the independence sequence (s0, s1, . . . , sα) equals the number of independent k-sets of vertices of G. We investigate constraints on the linear orderings of the terms of the independence sequence of well-covered graphs. In particular, we provide a counterexample to the recent u...

A path-factor in a graph G is spanning subgraph F of such that every component path. Let d and n be two nonnegative integers with ≥ 2. P -factor its each whose components path at least vertices. called covered if for any e ∈ E ( ), admits containing . , )-factor critical N ⊆ V ) | = the − graph. uniform In this paper, we verify following results: (i) An + 1)-connected order 3 ≥3 satisfies δ &gt...

Let G be a graph that is a subgraph of some n-dimensional hypercube Qn. For sufficiently large n, Stout [20] proved that it is possible to pack vertexdisjoint copies of G in Qn so that any proportion r < 1 of the vertices of Qn are covered by the packing. We prove an analogous theorem for edge-disjoint packings: For sufficiently large n, it is possible to pack edge-disjoint copies of G in Qn so...

The bicontraction of a vertex v of degree two in a graph, with precisely two neighbours v1 and v2, consists of shrinking the set {v1, v, v2} to a single vertex. The retract of a matching covered graph G, denoted by Ĝ, is the graph obtained from G by repeatedly bicontracting vertices of degree two. Up to isomorphism, the retract of a matching covered graph G is unique. If G is a brace on six or ...

A set A of vertices in an r-uniform hypergraph H is covered in H if there is some vertex u 6∈ A such that every edge of form {u} ∪ B, B ∈ A(r−1) is in H. Erdős and Moser (1970) determined the minimum number of edges in a graph on n vertices such that every k-set is covered. We extend this result to r-uniform hypergraphs on sufficiently many vertices, and determine the extremal hypergraphs. We a...