With ever growing databases containing multimedia data, indexing has become a necessity to avoid a linear search. We propose a novel technique for indexing multimedia databases in which entries can be represented as graph structures. In our method, the topological structure of a graph as well as that of its subgraphs are represented as vectors whose components correspond to the sorted laplacian...

The energy of a graph was introduced by Gutman in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. These are Cayley graphs on cyclic groups (i.e. there adjacency matrix is circulant) each of whose eigenvalues is an integer. Given an arbitrary prime power p, we determine all integral circu...

Let k be a perfect field and let K/k be a finite extension of fields. An arithmetic noncommutative projective line is a noncommutative space of the form ProjSK(V ), where V be a k-central two-sided vector space over K of rank two and SK(V ) is the noncommutative symmetric algebra generated by V over K defined by M. Van den Bergh [26]. We study the geometry of these spaces. More precisely, we pr...

It is known by Sahni [2] that the integral flow problem with overlapped bundles is NP-complete. We show that this problem remains NP-complete even if the bundles are disjoint. 1. Definition of the problem Let D = (N,E) be a directed graph with specified nodes s, t ∈ N . A mapping f : E → IN0 is called an integral flow, if for each node v ∈ N \{s, t}, ∑ (u,v)∈E f((u, v)) = ∑

We consider the 1-median problem in R with the Chebyshev-norm: Given n points with nonnegative weights, find a point that minimizes the sum of the weighted distances to the given points. We propose a combinatorial algorithm for this problem by reformulating it as a fractional b-matching problem. This graph-theoretical problem can be solved by a min-cost-flow algorithm. Moreover, we show that th...

Throughout this paper a graph G is assumed to be simple, i.e. a finite undirected graph without loops or multiple edges. Therefore, the characteristic polynomial of (the adjacency matrix of) G, denoted by PG(λ), has only real zeroes and this family of eigenvalues (the spectrum of G) will be represented as (λ1, λ2, . . . , λn), where λ1 ≥ λ2 ≥ · · · ≥ λn or in the form μ1 1 , μ2 2 , . . . , μm m...

A plane integral drawing of a planar graph G is a realization of G in the plane such that the vertices of G are mapped into distinct points and the edges of G are mapped into straight line segments of integer length which connect the corresponding vertices such that two edges have no inner point in common. We conjecture that plane integral drawings exist for all planar graphs, and we give parts...

In a bidirected graph, each end of each edge is independently oriented. We show how to express any column of the incidence matrix as a half-integral linear combination of any column basis, through a simplification, based on an idea of Bolker, of a combinatorial algorithm of Appa and Kotnyek. Corollaries are that the inverse of each nonsingular square submatrix has entries 0, ±12 , and ±1, and t...