In [8, 9] M. G. Corrales Garcia, D. M. Barquero, C. Martin Gonzalez, M. Siles Molina, J. F Solanilla Hernandez described the center of a Leavitt path algebra and characterized it in terms of the underlying graph. We offer a different characterization of the center. In particular, we prove that the Boolean algebra of central idempotents of a Leavitt path algebra of a finite graph is isomorphic t...

Bidirectional Path Tracing (BDPT) is a robust unbiased rendering algorithm that samples paths by connecting eye and light paths. By optimally combining different sampling strategies using Multiple Importance Sampling (MIS), BDPT efficiently renders scenes with complex light effects. However, BDPT does not map well on a streaming architecture such as the GPU; Stochastic path lengths lead to an u...

In this paper, we reduce the logspace shortest path problem to biconnected graphs; in particular, we present a logspace shortest path algorithm for general graphs which uses a logspace shortest path oracle for biconnected graphs. We also present a linear time logspace shortest path algorithm for graphs with bounded vertex degree and biconnected component size, which does not rely on an oracle. ...

An induced graphoidal cover of a graph G is a collection ψ of (not necessarily open) paths in G such that every path in ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in ψ, every edge of G is in exactly one path in ψ and every member of ψ is an induced cycle or an induced path. The minimum cardinality of an induced graphoidal cover of G is called the in...

An algorithm is described which constructs a long path containing a selected vertex x in a graph G. In hamiltonian graphs, it often finds a hamilton cycle or path. The algorithm uses crossovers of order k ≤ M , where M is a fixed constant, to build a longer and longer path. The method is based on theoretical methods often used to prove graphs hamiltonian.

For two vertices u and v in a graph G = (V, E), the detour distance D (u, v) is the length of a longest u – v path in G. A u – v path of length D (u, v) is called a u – v detour. For subsets A and B of V, the detour distance D (A, B) is defined as D (A, B) = min {D (x, y) : x ∈ A, y ∈ B}. A u – v path of length D (A, B) is called an A – B detour joining the sets A, B V where u ∈ A and v ∈ B. A...

Finding shortest paths and shortest distances between points on a surface S in three-dimensional space is a well-studied problem in differential geometry and computational geometry. The shortest path between two points on S is denoted a geodesic path on the surface and the shortest distance between two points on S is denoted a geodesic distance. In this survey, we consider the case where a disc...

An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted by rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. It was proved that computing rc(G) is an NP-Hard problem, as well as that even deciding whether a graph has rc(G) =...

In the gas station problem we want to find the cheapest path between two vertices of an n-vertex graph. Our car has a specific fuel capacity and at each vertex we can fill our car with gas, with the fuel cost depending on the vertex. Furthermore, we are allowed at most ∆ stops for refuelling. In this short paper we provide an algorithm solving the problem in O(∆n2 + n2 logn) steps improving an ...

The problems of miniiiwn Lg.: ana minimum vertex covers by paths results relate to papers by Galki-M&ram, Meyniel, Alspach-Pullman and mait resulti is contimed with partially ordered sets. are discussed. The others. One of tie NM+oak The terminology is rather standard, generally following Berge [3]. In any case where ar&iguity may arise we give +finiticns. Graphs alnd digraphs are f@ite, except...