Partitioning is a fundamental operation on graphs. In this paper we briefly review the basic concepts of graph partitioning and its relationship to digital mesh processing. We also elaborate on the connection between graph partitioning and spectral graph theory. Applications in computer graphics are described.

‎In addition to his countless contributions to spectral graph theory‎, some works of Dragos Cvetkovic are concerned with chemical problems‎. These are briefly outlined‎, ‎with emphasis on his collaboration with‎ ‎the present author‎.

In 2006, Espinola and Kirk made a useful contribution on combining fixed point theoryand graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using  the main idea of their work and the idea of combining fixed point theory on intuitionistic fuzzy metric spaces and graph theory, ...

The study of eigenvalues of graphs has a long history. Since the early days, representation theory and number theory have been very useful for examining the spectra of strongly regular graphs with symmetries. In contrast, recent developments in spectral graph theory concern the effectiveness of eigenvalues in studying general (unstructured) graphs. The concepts and techniques, in large part, us...

In previous work we defined a Quillen model structure, determined by cycles, on the category Gph of directed graphs. In this paper we give a complete description of the homotopy category of graphs associated to our model structure. We endow the categories of N-sets and Z-sets with related model structures, and show that their homotopy categories are Quillen equivalent to the homotopy category H...

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...

The global functional brain network (graph) is more suitable for characterizing brain states than local analysis of the connectivity of brain regions. Therefore, graph-theoretic approaches are the natural methods to study the brain. However, conventional graph theoretical analyses are limited due to the lack of formal statistical methods for estimation and inference for random graphs. For examp...

Most real networks are too large or they are not available for real time analysis. Therefore, in practice, decisions are made based on partial information about the ground truth network. It is of great interest to have metrics to determine if an inferred network (the partial information network) is similar to the ground truth. In this paper we develop a test for similarity between the inferred ...