a kernel $j$ of a digraph $d$ is an independent set of vertices of $d$ such that for every vertex $w,in,v(d),setminus,j$ there exists an arc from $w$ to a vertex in $j.$in this paper, among other results, a characterization of $2$-regular circulant digraph having a kernel is obtained. this characterization is a partial solution to the following problem: characterize circulant digraphs which hav...

By exploring the intelligent cooperation of unmanned aerial vehicle (UAV) swarms, formed flying ad-hoc networks (FANETs) can support a variety collaborative operations with real-time communications in emergency scenarios. To reduce prohibitively high routing overhead connectivity guaranteed multi-hop links, UAV swarms construct virtual backbone network (VBN) based on graph-theoretical <inline-f...

Let fα : {0, 1} → {0, 1} be one of four functions from two bits to one bit defined as fα(x1, x2) = δα1,x1δα2,x2 where α ∈ {0, 1} and x ∈ {0, 1} (The four different functions are label by the two bits of α.) (a) Prove that in order to exactly (no probability of failure) distinguish between these four functions, you need to query this function three times in the worst case. The function is 1 on o...

Abstrac t Set boolean operations between 2-dlmensional geometric objects are crucial in computational geometry and deserve rigorous treatments. We build up a simple and convergent system of rewrite rules modulo equations to cope with their design. This system is complete is the sense that it gives a detailed description for all particular cases. This specification leans on a new operation of la...