We present a robust skeleton-based action recognition method with graph convolutional network (GCN) that uses the new adjacency matrix, called Rank-GCN. In Rank-GCN, biggest change from previous approaches is how matrix generated to accumulate features neighboring nodes by re-defining “adjacency.” The which we call rank ranking all according metrics including Euclidean distance of...

A graph   is called integral if all eigenvalues of its adjacency matrix  are integers.  Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid sin S, xin G}$.  In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.

A universal adjacency matrix U of a graph G is a linear combination of the 0–1 adjacency matrix A, the diagonal matrix of vertex degrees D, the identity matrix I and the matrix J each of whose entries is 1. A main eigenvalue of U is an eigenvalue having an eigenvector that is not orthogonal to the all–ones vector. It is shown that the number of distinct main eigenvalues of U associated with a s...

Let $G = (V, E)$ be a simple graph. Denote by $D(G)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $A(G)$ the adjacency matrix of $G$. The  signless Laplacianmatrix of $G$ is $Q(G) = D(G) + A(G)$ and the $k-$th signless Laplacian spectral moment of  graph $G$ is defined as $T_k(G)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

We will discuss a few basic facts about the distribution of eigenvalues of the adjacency matrix, and some applications. Then we discuss the question of computing the eigenvalues of a symmetric matrix. 1 Eigenvalue distribution Let us consider a d-regular graph G on n vertices. Its adjacency matrix AG is an n× n symmetric matrix, with all of its eigenvalues lying in [−d, d]. How are the eigenval...

Abstract In this paper, we give the spectrum of a matrix by using the quotient matrix, then we apply this result to various matrices associated to a graph and a digraph, including adjacency matrix, (signless) Laplacian matrix, distance matrix, distance (signless) Laplacian matrix, to obtain some known and new results. Moreover, we propose some problems for further research. AMS Classification: ...

Objective: The symmetric encryption technique is one of the most important fields for securing communications between people. In order to produce complex ciphertext, we are introducing new enciphering with help Hamiltonian path, a self-invertible key matrix and decryption. Methods: There many kinds methods, like Caesar Cipher, Atbash Hill etc. All these methods use common encryption, while decr...

In this paper, we propose an algorithm which can improve Katz and Rosenschein's plan veriication algorithm. First, we represent the plan-like relations with adjacency lists and inverse adjacency lists to replace adjacency matrixes. Then, we present a method to avoid generating useless sub-graphs while generating the compressed set. Last, we compare two plan veriication algorithms. We not only p...

The Hales numbered n-dimensional hypercube and the corresponding adjacency matrix exhibit interesting recursive structures in n. These structures lead to a very simple proof of the well-known bandwidth formula for hypercube, whose proof was thought to be surprisingly difficult. A related problem called hypercube antibandwidth, for which Harper proposed an algorithm, is also reexamined in the li...

We examine the binary codes C2(Ai + I) from matrices Ai + I where Ai is an adjacency matrix of a uniform subset graph Γ(n, 3, i) of 3-subsets of a set of size n with adjacency defined by subsets meeting in i elements of Ω, where 0 ≤ i ≤ 2. Most of the main parameters are obtained; the hulls, the duals, and other subcodes of the C2(Ai + I) are also examined. We obtain partial PD-sets for some of...