Marked directed graphs

Marked Directed Graphs

Independent domination in directed graphs

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

Twin minus domination in directed graphs

Let $D=(V,A)$ be a finite simple directed graph. A function$f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (TMDF) if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for eachvertex $vin V$. The twin minus domination number of $D$ is$gamma_{-}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. Inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...

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...

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.