Predicting the wear performance of circular diamond saw in the process of sawing hard dimensional stone is an important step in reducing production costs in the stone sawing industry. In the present research work, the effective parameters on circular diamond saw wear are defined, and then the weight of each parameter is determined through adopting a fuzzy rock engineering system (Fuzzy RES) bas...

This paper is concerned with the paths and the cycles in d-dimensional tori with faulty vertices and/or edge. Let fv be the number of faulty vertices and fe be the number of faulty edges. It is shown that in any non-bipartite d-dimensional k1 × k2 × · · · kd torus with ki ≥ 3 for each 1 ≤ i ≤ d, (a) if fv + fe ≤ 2d − 3, there is a fault-free spanning path between any pair of non-faulty vertices...

We propose a configuration-free method to perform collective operations efficiently in dynamically changing topologies. Our collective operations are designed so that (1) they perform well when the topology is stable, (2) they complete successfully even when processors join or leave, and (3) they adapt to topology changes. We propose to create adaptive latency-aware spanning trees for short mes...

We study the Minimum Spanning Caterpillar Problem (MSCP) in a graph where each edge has two costs, spine (path) cost and leaf cost, depending on whether it is used as a spine or a leaf edge. The goal is to find a spanning caterpillar in which the sum of its edge costs is the minimum. We show that the problem has a linear time algorithm when a tree decomposition of the graph is given as part of ...

Let G be a graph and let f positive integer-valued function on V(G). In this paper, we show that if for all S⊆V(G), ω(G∖S)<∑v∈S(f(v)−2)+2+ω(G[S]), then has spanning tree T containing an arbitrary given matching such each vertex v, dT(v)≤f(v), where ω(G∖S) denotes the number of components G∖S ω(G[S]) induced subgraph G[S] with set S. This is improvement several results. Next, prove ω(G∖S)≤∑v∈S(f...

let $gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. denote by $upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. in the classes of graphs $gamma_{n,kappa}$ and $upsilon_{n,beta}$, the elements having maximum augmented zagreb index are determined.

A new method for proving Kirchhoff Matrix-Tree theorem, involving combinatorics of Grassmann variables, is developed. The theorem allows to evaluate the partition function of spanning trees on a given weighted graph, which emerges both in a limit of Potts Model, and of a free scalar fermion. The method generalizes to other counting problems beyond spanning trees: forests, hyper-trees and hyper-...