Characterizations of consistent marked graphs

Characterizations of Consistent Marked Graphs

A marked graph is a graph with a + or − sign on each vertex and is called consistent if each cycle has an even number of − signs. This concept is motivated by problems of communication networks and social networks. We present some new characterizations/recognition algorithms for consistent marked graphs.

A characterization of consistent marked graphs

A marked graph is obtained from a graph by giving each point either a positive or a negative sign. Beineke and Harary raised the problem of characterizing consistent marked graphs in which the product of the signs of the points is positive for every cycle. In this paper a characterization is given in terms of fundamental cycles of a cycle basis.

Characterizations of arboricity of graphs

The aim of this paper is to give several characterizations for the following two classes of graphs: (i) graphs for which adding any l edges produces a graph which is decomposible into k spanning trees and (ii) graphs for which adding some l edges produces a graph which is decomposible into k spanning trees. Introduction and Theorems The concept of decomposing a graph into the minimum number of ...

Marked Directed Graphs

Morphisms on Marked Graphs

Abstract. Many kinds of morphisms on Petri nets have been defined and studied. They can be used as formal techniques supporting refinement/abstraction of models. In this paper we introduce a new notion of morphism on marked graphs, a class of Petri nets used for the representation of systems having deterministic behavior. Such morphisms can indeed be used to represent a form of abstraction on m...