The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the s...

One of the most important issues for Muslim philosophers is the continuous imaginal world and its relationship with the discontinuous imaginative faculty. The continuous imaginal world is a perceptive faculty of the soul known as the faculty of imagination. The discontinuous imaginative faculty is the order of the universe called the imaginal world, which Muslim philosophers have portrayed in a...

This article presents the basic place/transition net structure definition for building various types of Petri nets. The basic net structure fields include places, transitions, and arcs (place-transition, transition-place) which may be supplemented with other fields (e.g., capacity, weight, marking, etc.) as needed. The theorems included in this article are divided into the following categories:...

In the Capacitated Arc Stabbing problem (CAS) we are given a set of arcs and a set of points on a circle. We say that a point p covers, or stabs, an arc A if p is contained in A. Each point has a weight and a capacity that determines the number of arcs it may cover. The goal is to find a minimum weight set of points that stabs all the arcs. CAS models a periodic multiitem lot sizing problem in ...

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊆V . An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P . (If Γ is not abelian, we sum the labels in their order along the path.) We give an efficient algorithm for finding ...

Given a weighted directed graph G = (V,A), the minimum feedback arc set problem consists of finding a minimum weight set of arcs A ⊆ A such that the directed graph (V,A \ A) is acyclic. Similarly, the minimum feedback vertex set problem consists of finding a minimum weight set of vertices containing at least one vertex for each directed cycle. Both problems are NP-complete. We present simple co...

Let G = (V,A,g) be a strongly connected weighted graph. We say that G is max-balanced if for every cut W, the maximum weight over arcs leaving W equals the maximum weight over arcs entering W. A subgraph H of G is max-sufficient if (or every cut W, the maximum weight over a.rcs of G leaving W is attained at some arc of H. A tower T = (CI,C., ... ,C,) is a sequence of arc-sets of G where C'+ I i...