The shortest paths problem on weighted directed graphs is one of the basic network optimization problems. Its importance is mainly due to its applications in various areas, such as communication and transportation. Given a source node s in a weighted directed graph G, with n nodes and m arcs, the single-source shortest path problem (SSSP, for short) from s is the problem of finding the minimum ...

A graph is called symmetric if its full automorphism group acts transitively on the set of arcs. The Cayley graph $Gamma=Cay(G,S)$ on group $G$ is said to be normal symmetric if $N_A(R(G))=R(G)rtimes Aut(G,S)$ acts transitively on the set of arcs of $Gamma$. In this paper, we classify all connected tetravalent normal symmetric Cayley graphs of order $p^2q$ where $p>q$ are prime numbers.

Outerstring graphs are the intersection graphs of curves that lie inside a disk such that each curve intersects the boundary of the disk in one of its endpoints. Outerstring graphs were introduced in 1991 and are amongst the most general classes of intersection graphs studied, including among others, chordal graphs and interval filament graphs. To date no polynomial time algorithm is known for ...

In a large, dense network, the computation of the ‘distances’, i.e., the shortest path lengths between all pairs of nodes, can take a long time with algorithms known from the literature. We present two all-pairs shortest path algorithms, based on the equations of Bellman. These algorithms run fast, much faster than indicated by their time complexity bound of O(n2m), where n is the number of nod...

karun river with a length of about 890 km is considered as a main river in the country. in this paper, types of karun’s screws regarding to the geometric factors of radius of curvature and chord length were identified by fitting circles with the arcs of the river’s axis. river’s arcs were classified into simple and compound screws. then, by formation of the database consist of topographic...

the notion of strong arcs in a fuzzy graph was introduced bybhutani and rosenfeld in [1] and fuzzy end nodes in the subsequent paper[2] using the concept of strong arcs. in mordeson and yao [7], the notion of“degrees” for concepts fuzzified from graph theory were defined and studied.in this note, we discuss degrees for fuzzy end nodes and study further someproperties of fuzzy end nodes and fuzz...

the arc costs are assumed to be online parameters of the network and decisions should be made while the costs of arcs are not known. the policies determine the permitted nodes and arcs to traverse and they are generally defined according to the departure nodes of the current policy nodes. in on-line created tours arc costs are not available for decision makers. the on-line traversed nodes are f...

Recursive neural networks are conceived for processing graphs and extend the well-known recurrent model for processing sequences. In Frasconi et al. (1998), recursive neural networks can deal only with directed ordered acyclic graphs (DOAGs), in which the children of any given node are ordered. While this assumption is reasonable in some applications, it introduces unnecessary constraints in ot...