Given a set R of robots, each one located at different vertex an infinite regular tessellation graph, we aim to explore the Arbitrary Pattern Formation (APF) problem. multiset F grid vertices such that |R|=|F|, APF asks for distributed algorithm moves robots so as reach configuration similar F. Similarity means must be disposed regardless translations, rotations, reflections. So far, possible g...

triangular graphs 7] (in which every vertex v; v 6 = v 1 ; v 2 ; v n , has 2 incoming and 1 outgoing edge in the acyclic orientation). Another observation is that the canonical ordering, presented in section 4, gives a simple algorithm to test whether a planar triangular graph is 4-connected. An interesting research eld is to problem of computing a canonical ordering of a 4-connected planar gra...

Let be a graph with and are the set of its vertices edges, respectively. Total edge irregular -labeling on is map from to satisfies for any two distinct edges have weights. The minimum which labeling spoken as strength total labeling, represented by . In this paper, we discuss tes triangular grid graphs, spanning subgraphs, Sierpiński gasket graphs.

The triangular array of binomial coefficients, or Pascal’s triangle, is formed by starting with an apex of 1. Every row of Pascal’s triangle can be seen as a line-graph, to each node of which the corresponding binomial coefficient is assigned. We show that the binomial coefficient of a node is equal to the number of ways the line-graph can be constructed when starting with this node and adding ...

In this paper, we first prove that when the associated graph of a polynomial set is chordal, particular triangular computed by general algorithm in top-down style for computing decomposition has an as subgraph chordal graph. Then Wang's method and subresultant-based regular style, all sets appearing process with any these algorithms have graphs subgraphs These theoretical results can be viewed ...

We consider the question: “What is the smallest degree that can be achieved for a plane spanner of a Euclidean graph E?” The best known bound on the degree is 14. We show that E always contains a plane spanner of maximum degree 6 and stretch factor 6. This spanner can be constructed efficiently in linear time given the Triangular Distance Delaunay triangulation introduced by Chew.

In this paper we consider the ip operation for combinatorial pointed pseudo-triangulations where faces have size 3 or 4, so-called combinatorial 4-PPTs. We show that every combinatorial 4-PPT is stretchable to a geometric pseudo-triangulation, which in general is not the case if faces may have size larger than 4. Moreover, we prove that the ip graph of combinatorial 4-PPTs with triangular outer...

Non-binary codes of length ( n 2 ) , dimension n or n − 1, minimum weight n − 1 or 2n − 4, respectively, that can be obtained from designs associated with the complete graph on n vertices and their line graphs, the triangular graphs, are examined. The parameters of the codes and their automorphism groups for any odd prime are obtained and PD-sets inside the symmetric group Sn are found for full...

Critical path method is a network based method planned for development and organization of complex project in real world application. In this paper, a new methodology has been made to find the critical path in a directed acyclic graph, whose activity time uncertain. The vague parameters in the network are represented by intuitionistic triangular fuzzy numbers, instead of crisp numbers. A new pr...