We consider computational problems on covering graphs with bicliques (complete bipartite subgraphs). Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the graph can be covered with at most k bicliques; the biclique partition problem is defined similarly with the additional condition that the bicliques are required to be mutually edge-disjoint. The biclique ...

We strengthen the closure concept for Hamilton-connectedness in claw-free graphs, introduced by the second and fourth authors, such that the strong closure GM of a claw-free graph G is the line graph of a multigraph containing at most two triangles or at most one double edge. Using the concept of strong closure, we prove that a 3-connected claw-free graph G is Hamilton-connected if G satisfies ...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

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...