This paper gives tight upper bound on the largest eigenvalue q (G) of the signless Laplacian of graphs with no paths of given order. Thus, let Sn,k be the join of a complete graph of order k and an independent set of order n− k, and let S n,k be the graph obtained by adding an edge to Sn,k. The main result of the paper is the following theorem: Let k ≥ 1, n ≥ 7k, and let G be a graph of order n...

1. Introduction. A graph G consists of a set 7 of elements called vertices together with a set E of elements called edges, the two sets having no element in common. With each edge there are associated either one or two vertices called its ends. In this paper we consider only graphs in which each edge has two distinct ends. We call such a graph oriented if one end of each edge is distinguished a...

In many applications, the underlying data (the web, an XML document, or a relational database) can be seen as a graph. These graphs may be enriched with weights, associated with the nodes and edges of the graph, denoting application specific desirability/penalty assessments, such as popularity, trust, or cost. A particular challenge when considering such weights in query processing is that resu...

Understanding complex relationships among heterogeneous biological data is one of the fundamental goals in biology. In most cases, diverse biological data are stored in relational databases, such as MySQL and Oracle, which store data in multiple tables and then infer relationships by multiple-join statements. Recently, a new type of database, called the graph-based database, was developed to na...

The effective processing of semi-structured data queries is a preliminary part of data mining stage. XML queries employ regular path expressions to find structural patterns within XML documents. The operation of structural join is a crucial part of XML query processing. Existing approaches reduce complex join expressions to several binary structural joins. In this paper, we are proposing a new ...

We characterize well-founded algebraic lattices by means of forbidden subsemilattices of the join-semilattice made of their compact elements. More specifically, we show that an algebraic lattice L is well-founded if and only if K(L), the join-semilattice of compact elements of L, is well-founded and contains neither [ω], nor Ω(ω∗) as a join-subsemilattice. As an immediate corollary, we get that...

The k-wheel Wk is the graph obtained as a join of a vertex and the cycle of length k. It is proved that a subdivided wheel G embeds isometrically into a hypercube if and only if G is the subdivision graph S(K4) of K4 or G is obtained from the wheel Wk (k¿ 3) by subdividing any of its outer-edges with an odd number of vertices. c © 2003 Elsevier B.V. All rights reserved.

Abstract. Renner has defined an order on the set of partial injective functions from [n] = {1, . . . , n} to [n]. This order extends the Bruhat order on the symmetric group. The poset Pn obtained is isomorphic to a set of square matrices of size n with its natural order. We give the smallest lattice that contains Pn. This lattice is in bijection with the set of alternating matrices. These matri...

A graft is a graph G = (V,E) together with a set T ⊆ V of even cardinality. A T-cut of G is an edge cut δ(X) for which |X ∩T | is odd. A T-join of G is a set of edges S ⊆ E with the property that a vertex of the graph (V, S) has odd degree if and only if it is in T . A T-join packing of G is a set of pairwise disjoint T-joins. Let τ(G) be the size of the smallest T-cut of G and let ν(G) be the ...