Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

Similarity Learning of Manifold Data

Abstract: Without constructing adjacency graph for neighborhood, we propose a method to learn similarity among sample points of manifold in Laplacian embedding (LE) based on adding constraints of linear reconstruction and least absolute shrinkage and selection operator type minimization. Two algorithms and corresponding analyses are presented to learn similarity for mix-signed and nonnegative data respectively. The similarity learning method is further extended to kernel spaces. The experiments on both synthetic and real world benchmark data sets demonstrate that the proposed LE with new similarity has better visualization and achieves higher accuracy in classification.

Generation of Epicyclic Gear Trains of One Degree of Freedom

Abstract: New planetary gear trains (PGTs) are generated using graph theory. A geared kinematic chain is converted to a graph and a graph in turn is algebraically represented by a vertex-vertex adjacency matrix. Checking for isomorphism needs to be an integral part of the enumeration process of PGTs. Hamming matrix is written from the adjacency matrix, using a set of rules, which is adequate to detect isomorphism in PGTs. The present work presents the twin objectives of testing for isomorphism and compactness using the Hamming matrices and moment matrices.

Cospectral graphs and the generalized adjacency matrix

Abstract: Let J be the all-ones matrix, and let A denote the adjacency matrix of a graph. An old result of Johnson and Newman states that if two graphs are cospectral with respect to yJ - A for two distinct values of y, then they are cospectral for all y. Here we will focus on graphs cospectral with respect to yJ - A for exactly one value widehat{y} of y. We call such graphs widehat{y}-cospectral. It follows that widehat{y} is a rational number, and we prove existence of a pair of widehat{y}-cospectral graphs for every rational widehat{y}. In addition, we generate by computer all widehat{y}-cospectral pairs on most nine vertices. Recently, Chesnokov and the second author constructed pairs of widehat{y}-cospectral graphs for all rational widehat{y}{in}(0,1), where one graph is regular and the other one is not. This phenomenon is only possible for the mentioned values of widehat{y}, and by computer we find all such pairs of widehat{y}-cospectral graphs on at most eleven vertices.