Local properties of graphs

Local Properties of Triangular Graphs

In the paper triangular graphs are discussed. The class of triangular graphs is of special interest as unifying basic features of complete graphs with trees and being used on many various occasions. They model processor networks in which local computations can be easily implemented. The main issue addressed in the paper is to characterize class of triangular graphs (defined globally) by local m...

Local properties of geometric graphs

We introduce a new property for geometric graphs: the local diameter. This property is based on the use of the region counting distances introduced by Demaine, Iacono and Langerman as a generalization of the rank difference. We use it as a characterization of the local density of the vertices. We study the properties of those distances, and show that there is a strong relation between region co...

Extremal problems for local properties of graphs

Structural properties of fuzzy graphs

Matroids are important combinatorial structures and connect close-lywith graphs. Matroids and graphs were all generalized to fuzzysetting respectively. This paper tries to study  connections betweenfuzzy matroids and fuzzy graphs. For a given fuzzy graph, we firstinduce a sequence of matroids  from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matro...

Local chromatic number and topological properties of graphs

The local chromatic number of a graph, introduced by Erdős et al. in [3], is the minimum number of colors that must appear in the closed neighborhood of some vertex in any proper coloring of the graph. This talk, based on the papers [13, 14, 15], would like to survey some of our recent results on this parameter. We give a lower bound for the local chromatic number in terms of the lower bound of...