Showing papers on "Spectral graph theory published in 1992"

Walk Generating Functions, Christoffel-Darboux Identities and the Adjacency Matrix of a Graph

Abstract: In this work we show that that many of the basic results concerning the theory of the characteristic polynomial of a graph can be derived as easy consequences of a determinantal identity due to Jacobi As well as improving known results, we are also able to derive a number of new ones A combinatorial interpretation of the Christoffel-Darboux identity from the theory of orthogonal polynomials is also presented Finally, we extend some work of Tutte on the reconstructibility of graphs with irreducible characteristic polynomials

Conflict-free broadcasting algorithms for graph traversals and their applications

Abstract: In this paper, using an adapted graph representation: double links adjacency arrays, we present conflict-free algorithms for solving some graph proglems under the single-channel broadcast communication model. These graph problems include depth first search, breadth first search, finding spanning trees, finding connected components, and finding articulation points and bridges. All the proposed algorithms broadcast 2n - 1 messages and run in O(n^2 / p) time when p processors are used, where 1 < p @? n and n is the number of vertices. The total space requirements is O(n^2). When the adjacency matrix is used to represent a graph, solving these problems requires O(n^2) sequential time. Since the adjacency matrix representation can be converted into the double links adjacency arrays representation in O(n^2 / p) time using p processors, the proposed algorithms are all cost-optimal. The result of this paper makes a significant improvement over Yang, Lee and Chen's work. Also, this paper reveals a fact that well-constructed data structures are useful in designing conflict-free broadcasting algorithms.