Note on a Helicopter Search Problem on Graphs

Note on a helicopter search problem on graphsFedor

We consider a search game on a graph in which one cop in a helicopter ying from vertex to vertex tries to catch the invisible robber. The existence of the winning program for the cop in this problem depends only on the robber's speed. We investigate the problem of nding the minimal robber's speed which prevents the cop from winning. For this parameter we give tight bounds in terms of the linkag...

A note on polyomino chains with extremum general sum-connectivity index

The general sum-connectivity index of a graph $G$ is defined as $chi_{alpha}(G)= sum_{uvin E(G)} (d_u + d_{v})^{alpha}$ where $d_{u}$ is degree of the vertex $uin V(G)$, $alpha$ is a real number different from $0$ and $uv$ is the edge connecting the vertices $u,v$. In this note, the problem of characterizing the graphs having extremum $chi_{alpha}$ values from a certain collection of polyomino ...

A Note on Strongly Quotient Graphs

A Tabu Search Method for a New Bi-Objective Open Shop Scheduling Problem by a Fuzzy Multi-Objective Decision Making Approach (RESEARCH NOTE)

This paper proposes a novel, bi-objective mixed-integer mathematical programming for an open shop scheduling problem (OSSP) that minimizes the mean tardiness and the mean completion time. To obtain the efficient (Pareto-optimal) solutions, a fuzzy multi-objective decision making (fuzzy MODM) approach is applied. By the use of this approach, the related auxiliary single objective formulation can...

A note on vague graphs

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.