let $n,t_1,...,t_k$ be distinct positive integers. a toeplitz graph $g=(v, e)$ denoted by $t_n$ is a graph, where $v ={1,...,n}$ and $e= {(i,j) : |i-j| in {t_1,...,t_k}}$.in this paper, we present some results on decomposition of toeplitz graphs.

We extend the resistance distance kernel to the domain of signed dissimilarity values, and show how it can be applied to collaborative rating prediction. The resistance distance is a graph kernel inspired by electrical network models where edges of a graph are interpreted as electrical resistances. We model the similarity between users of a large collaborative rating database using this signed ...

This is an expository survey of the uses of matrices in the theory of simple graphs with signed edges. A signed simple graph is a graph, without loops or parallel edges, in which every edge has been declared positive or negative. For many purposes the most significant thing about a signed graph is not the actual edge signs, but the sign of each circle (or ‘cycle’ or ’circuit’), which is the pro...

Signed link prediction in social networks aims to reveal the underlying relationships (i.e., links) among users nodes) given their existing positive and negative interactions observed. Most of prior efforts are devoted learning node embeddings with graph neural (GNNs), which preserve signed network topology by message-passing along edges facilitate downstream task. Nevertheless, graph-based app...

We determine the maximum order of an element in critical group a strongly regular graph, and show that it achieves spectral bound due to Lorenzini. extend result all graphs with exactly two non-zero Laplacian eigenvalues, study signed graph version problem. also monodromy pairing on groups, suggest approach structure these groups using pairing.

We present a decomposition formula for the weighted zeta function of an irregular covering of a graph by its weighted L-functions. Moreover, we give a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph. As an application, we discuss the structure of balanced coverings of signed graphs.

This paper surveys recent development of concepts related to coloring signed graphs. Various approaches are presented and discussed.

This paper studies learning meaningful node representations for signed graphs, where both positive and negative links exist. problem has been widely studied by meticulously designing expressive graph neural networks, as well capturing the structural information of through traditional structure decomposition methods, e.g., spectral theory. In this paper, we propose a novel representation framewo...