A Hamiltonian path of a graph is a simple path which visits each vertex of the graph exactly once. The Hamiltonian path problem is to determine whether a graph contains a Hamiltonian path. A graph is called Hamiltonian connected if there exists a Hamiltonian path between any two distinct vertices. In this paper, we will study the Hamiltonian connectivity of rectangular supergrid graphs. Supergr...

in this paper, some elementary operations on triangular fuzzynumbers (tfns) are defined. we also define some operations on triangularfuzzy matrices (tfms) such as trace and triangular fuzzy determinant(tfd). using elementary operations, some important properties of tfms arepresented. the concept of adjoints on tfm is discussed and some of theirproperties are. some special types of tfms (e.g. pu...

In this paper, we have shown that collection of paths P i n where n is odd, cycle, triangular snake, quadrilateral snake, P 2 n are even sequential harmonious graph and also we prove that the cycle Cn be a cycle u1, u2, · · · , un is an even sequential harmonious graph. Let G be a graph with V (G) = V (Cn) ∪ {wi : 1 ≤ i ≤ n}, E(G) = E(Cn) ∪ {uiwiui−1wi : 1 ≤ i ≤ n}, then G is an even sequential...

A novel algorithm for solving in parallel a sparse triangular linear system on a graphical processing unit is proposed. It implements the solution of the triangular system in two phases. First, the analysis phase builds a dependency graph based on the matrix sparsity pattern and groups the independent rows into levels. Second, the solve phase obtains the full solution by iterating sequentially ...

A graceful labelling of a graph with n edges is a vertex labelling where the induced set of edge weights is {1, . . . , n}. A near graceful labelling is almost the same, the difference being that the edge weights are {1, 2, . . . , n − 1, n + 1}. In both cases, the weight of an edge is the absolute difference between its two vertex labels. Rosa [8] in 1988 conjectured that all triangular cacti ...

An approach for solving sparse triangular systems of equations on highly parallel computers employs a partitioned representation of the inverse of the triangular matrix so that the solution can be obtained by a series of matrix-vector multiplications. This approach requires a number of global communication steps that is proportional to the number of factors in the partitioning. The problem of n...

Article history: Received 23 March 2010 Accepted 4 July 2011 Available online 23 July 2011

We consider an extension of the triangular-distance Delaunay graphs (TD-Delaunay) on a set P of points in general position in the plane. In TD-Delaunay, the convex distance is defined by a fixed-oriented equilateral triangle 5, and there is an edge between two points in P if and only if there is an empty homothet of 5 having the two points on its boundary. We consider higher-order triangular-di...

The Shannon capacity of a graph G is c(G) = supd>1(α(G d)) 1 d , where α(G) is the independence number of G. The Shannon capacity of the Kneser graph KGn,r was determined by Lovász in 1979, but little is known about the Shannon capacity of the complement of that graph when r does not divide n. The complement of the Kneser graph, KGn,2, is also called the triangular graph Tn. The graph Tn has th...