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 D=(V(D),A(D)) be a finite, simple digraph and k positive integer. A function f:V(D)→{0,1,2,…,k+1} is called [k]-Roman dominating (for short, [k]-RDF) if f(AN−[v])≥|AN−(v)|+k for any vertex v∈V(D), where AN−(v)={u∈N−(v):f(u)≥1} AN−[v]=AN−(v)∪{v}. The weight of [k]-RDF f ω(f)=∑v∈V(D)f(v). minimum on D the domination number, denoted by γ[kR](D). For k=2 k=3, we call them double Roman number tr...

A double Roman dominating function on a graph G=(V,E) is f:V?{0,1,2,3}, satisfying the condition that every vertex u for which f(u)=1 adjacent to at least one assigned 2 or 3, and with f(u)=0 3 two vertices 2. The weight of f equals sum w(f)=?v?Vf(v). minimum G called domination number ?dR(G) G. We obtain tight bounds in some cases closed expressions generalized Petersen graphs P(ck,k). In shor...

A Roman domination function on a graph G is a function r : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman function is the value r(V (G)) = ∑ u∈V (G) r(u). The Roman domination number γR(G) of G is the minimum weight of a Roman domination function on G . "Roman Criticality" has been ...

A edge 2-rainbow dominating function (E2RDF) of a graph G is a ‎function f from the edge set E(G) to the set of all subsets‎ ‎of the set {1,2} such that for any edge.......................

QMNF is a QoS-aware multicast routing protocol using N-hop dominating flooding and built upon a layered routing architecture. In this architecture, QMNF invites the N-hop flooding component and the shortest path routing table from OSPF by open signaling interfaces, floods the path-probing packets, and employs a two-pass resource reservation scheme to avoid unnecessary resource reservation. The ...

This paper describes a distributed algorithm (generalized d-CDS) for producing a variety of d-dominating sets of nodes that can be used to form the backbone of an ad hoc wireless network. In special cases (ordinary d-CDS), these sets are also d-hop connected and has a desirable “shortest path property”. Routing via the backbone created is also discussed. The algorithm has a “constant-time” comp...

An independent Roman dominating function (IRD-function) on a graph G is f : V ( ) → {0, 1, 2} satisfying the conditions that (i) every vertex u for which = 0 adjacent to at least one v 2, and (ii) set of all vertices assigned non-zero values under independent. The weight an IRD-function sum its over vertices, domination number i R minimum . In this paper, we initiate study bondage b iR having c...

Correspondence to Dr Wolfgang Wagner; [email protected] Visiting Ravenna, this ancient town near the Adriatic Sea in Italy, cannot be called anything but a feast in culture. From AD 402 to AD 476, it was the capital of the Western Roman Empire. The city and its harbour later became the Italian stronghold of the Eastern Roman Empire (Constantinople/Istanbul). No wonder that busloads of tour...