A connected dominating set of a graph G = (V, E) is a subset of vertices CD ⊆ V such that every vertex not in CD is adjacent to at least one vertex in CD, and the subgraph induced by CD is connected. We show that, given an arc family F with endpoints sorted, a minimum-cardinality connected dominating set of the circular-arc graph constructed from F can be computed in O(|F |) time.

In the article m dimensional lexicographic noncooperative games   ) ,..., ( 1 m   are defined for the players’ } ,..., 2 , 1 { n N  for which there exists a characteristic function T m v v v v ) ,..., , ( 2 1  . Some main features are proved of v function in a lexicographic case. A lexicographic cooperative game is called a couple   v N , , where v is a real vectorfunction on N subsets ...

This paper proposes and analyzes energy efficient Convex Hull based Minimum Connected Dominating Set [CHMCDS] algorithm. The algorithm achieves energy efficiency, bandwidth efficiency, reliability and robustness by reducing redundant rebroadcasts of control packets in the network. The Connected Dominating Set (CDS) is widely used as a virtual backbone or Spine in mobile ad-hoc networks for the ...

Given a graph $$G=(V,E)$$ and an integer k, the Minimum Membership Dominating Set (MMDS) problem seeks to find dominating set $$S \subseteq V$$ of G such that for each $$v \in , $$\vert N[v] \cap S\vert $$ is at most k. We investigate parameterized complexity obtain following results MMDS problem. First, we show NP-hard even on planar bipartite graphs. Next, W[1]-hard parameter pathwidth (and t...