The corona G◦H of two graphs G and H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining each i-th vertex of G to every vertex in the i-th copy of H. The neighborhood coronaG⋆H of two graphs G and H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the neighbors of the i-th vertex of G to every vertex in the i-th copy of H. In this p...

We study networks that display community structure--groups of nodes within which connections are unusually dense. Using methods from random matrix theory, we calculate the spectra of such networks in the limit of large size, and hence demonstrate the presence of a phase transition in matrix methods for community detection, such as the popular modularity maximization method. The transition separ...

Recognition of human pose is an actual problem in computer vision. To increase the reliability of the recognition it is proposed to use structured information in the form of graphs. The spectrum of graphs is applied for the comparison of the structures. Image skeletonization is used to construct graphs. Line segments are the nodes of the graph. The end point of line segments are the edges of th...

Our research focuses on developing design-oriented analytical tools that enable us to better understand how a network comprising dynamic and static elements behaves when it is set in oscillatory motion, and how the interconnection topology relates to the spectral properties of the system. Such oscillatory networks are ubiquitous, extending from miniature electronic circuits to large-scale power...

Numerical comparison of spaces with one another is often achieved with set scalar measures such as global and local integration, connectivity, etc., which capture a particular quality of the space but therefore lose much of the detail of its overall structure. More detailed methods such as graph edit distance are difficult to calculate, particularly for large plans. This paper proposes the use ...

The spectrum of a matrix M is the multiset that contains all the eigenvalues of M. If M is a matrix obtained from a graph G, then the spectrum of M is also called the graph spectrum of G. If two graphs has the same spectrum, then they are cospectral (or isospectral) graphs. In this paper, we compare four spectra of matrices to examine their accuracy in protein structural comparison. These four ...

Numerical comparison of spaces with one another is often achieved with set scalar measures such as global and local integration, connectivity, etc., which capture a particular quality of the space but therefore lose much of the detail of its overall structure. More detailed methods such as graph edit distance are difficult to calculate, particularly for large plans. This paper proposes the use ...

a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...