in this paper rst we dene the notions of positive implicativehyper mv -ideals of types 1,2,3 and 4 in hyper mv -algebras and we investigatethe relationship between of them . then by some examples we show that thesenotions are not equivalent. finally we give some relations between these notionsand the notions of (weak) hyper mv -ideals and (weak) hyper mv -deductivesystems of hyper mv -algebras.

The Hosoya polynomial of a graph, H(G, z), has the property that its first derivative, evaluated at z = 1, equals the Wiener index, i.e., W(G) = H’(G, 1). In this paper, an equation is presented that gives the hyper-Wiener index, WW(G), in terms of the first and second derivatives of H(G,z). Also defined here is a hyper-Hosoya polynomial, HH(G,r), which has the property WW(G) = HH’(G, l), analo...

A proper coloring of the vertices of a graph is called a star coloring if every two color classes induce a star forest. Star colorings are a strengthening of acyclic colorings, i.e., proper colorings in which every two color classes induce a forest. We show that every acyclic k-coloring can be refined to a star coloring with at most (2k2 − k) colors. Similarly, we prove that planar graphs have ...

With the increasing availability and scale of graph data from Web 2.0, graph partitioning becomes one of efficient preprocessing techniques to balance the computing workload. Since the cost of partitioning the entire graph is strictly prohibitive, there are some recent tentative works towards streaming graph partitioning which can run faster, be easily paralleled, and be incrementally updated. ...

This paper is concerned with the hybridization of two graph coloring heuristics (Saturation Degree and Largest Degree), and their application within a hyperheuristic for exam timetabling problems. Hyper-heuristics can be seen as algorithms which intelligently select appropriate algorithms/heuristics for solving a problem. We developed a Tabu Search based hyper-heuristic to search for heuristic ...

In this paper, we propose a specific structure in the star graph for local diagnosis under the PMC model. We design an adaptive local diagnosis algorithm for a star graph Sn. We prove that Sn is (n − 1)-diagnosable with our proposed algorithm under the PMC model. Moreover, with our algorithm, a diagnosis is completed in three test rounds.

The problem of solving a linear system of equations is widely encountered in many fields of science and engineering. In this paper, we present a parallel algorithm to solve the above problem on a star graph. The proposed solution (i) is based on a variant of the Gaussian elimination algorithm (GE) called the successive Gaussian elimination algorithm (SGE) (IEE Proc. Comput. Digit. Tech. 143 (4)...

Let G be a graph with chromatic number (G) and maximum degree (G). A star colouring of G is a function that assigns a colour to each vertex such that adjacent vertices receive distinct colours, and there is no bichromatic 4-vertex path. The star chromatic number st(G) is the minimum number of colours in a star colouring of G. Star colourings of subdivisions of graphs are investigated. Let G0 be...

We prove some Schur positivity results for the chromatic symmetric function X G of a (hyper)graph G, using connections to group algebra group. The first such connection works (hyper)forests F: we describe coefficients F in terms eigenvalues product Hermitian idempotents algebra, one factor each edge (a more general formula similar shape holds all chordal graphs). Our main application this techn...