A {em Roman dominating function} on a graph $G$ is a function $f:V(G)rightarrow {0,1,2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A {em total Roman dominating function} is a Roman dominating function with the additional property that the subgraph of $G$ induced by the set of all vertices of positive weight has n...

a roman dominating function (rdf) on a graph g = (v,e) is defined to be a function 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. a set s v is a restrained dominating set if every vertex not in s is adjacent to a vertex in s and to a vertex in . we define a restrained roman dominating function on a graph g = (v,e) to be ...

For every positive integer k, a set S of vertices in a graph G = (V;E) is a k- tuple dominating set of G if every vertex of V -S is adjacent to at least k vertices and every vertex of S is adjacent to at least k - 1 vertices in S. The minimum cardinality of a k-tuple dominating set of G is the k-tuple domination number of G. When k = 1, a k-tuple domination number is the well-studied domination...

Abstract It often has been an illusion that Filipinos lack indigeneity due to the ties with United States since 1898. Lost in these mists were indigenous agendas lay underneath official narratives. The article presents a background and then examines administration of Elpidio Quirino, president Philippines from 1948 1953, particularly his neutralist Pacific Pact initiative failed use military fo...

Efficient routing among a set of mobile hosts (also called nodes) is one of the most important functions in ad hoc wireless networks. Routing based on a connected dominating set is a promising approach, where the search space for a route is reduced to the nodes in the set. A set is dominating if all the nodes in the system are either in the set or neighbors of nodes in the set. In this paper, w...

Commons-based peer production – the distributed creation of freely accessible information resources through the mass aggregation of many contributions – represents a modality of collective intelligence that integrates the use of digital communication networks and information technologies [Benkler 2006; Benkler et al. 2013]. Peer production projects like Wikipedia and Linux have inspired numerou...

We develop a model of oligarchy subject to elite competition. Even when all members of the elite share an economic interest in labor repression, competition for control of the state can drive a wedge between the incentives of old and new elites. Thus ‘the iron law of oligarchy’–that all elite members share an overriding interest in repressive institutions–can be bent in various ways. New elites...