Note on a helicopter search problem on graphs

Note on a Helicopter Search Problem on Graphs

We consider a search game on a graph in which one cop in a helicopter flying 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 finding the minimal robber’s speed which prevents the cop from winning. For this parameter we give tight bounds in terms of the li...

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 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.

A Note on Strongly Quotient Graphs

A note on 3-Prime cordial graphs

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....