Distance-hereditary graphs are graphs in which every two vertices have the same distance in every connected induced subgraph containing them. This paper studies distance-hereditary graphs from an algorithmic viewpoint. In particular, we present linear-time algorithms for finding a minimum weighted connected dominating set and a minimum vertex-weighted Steiner tree in a distance-hereditary graph...

In recent years,MANET gain a significant attention for the potential application in battlefield, disaster relief, traffic monitoring and environment monitoring. Construction and maintain of virtual backbone, and energy effective routing in mobile ad hoc wireless network come to be the basic and main problem in MANET. This paper proposed the efficient ENMCDS algorithm for constructing the minimu...

188 Abstract-The lifetime of battery operated wireless sensor networks can be prolonged by energy aware maintenance of the virtual backbone. The energy of a node is depleted quickly during communication and network failure is most likely to occur when the energy of a Minimum Connected Dominating Set (MCDS) node is exhausted. The reconstruction of an alternate backbone without the depleted node ...

For a connected graph G and any non-empty S ⊆ V (G), S is called a weakly connected dominating set of G if the subgraph obtained from G by removing all edges each joining any two vertices in V (G) \ S is connected. The weakly connected domination number γw(G) is defined to be the minimum integer k with |S| = k for some weakly connected dominating set S of G. In this note, we extend a result on ...

A hub set in a graph G is a set U ⊆ V (G) such that any two vertices outside U are connected by a path whose internal vertices lie in U . We prove that h(G) ≤ hc(G) ≤ γc(G) ≤ h(G) + 1, where h(G), hc(G), and γc(G), respectively, are the minimum sizes of a hub set in G, a hub set inducing a connected subgraph, and a connected dominating set. Furthermore, all graphs with γc(G) > hc(G) ≥ 4 are obt...

This paper introduces a novel framework for generating pictorial storylines for given topics from text and image data on the Internet. Unlike traditional text summarization and timeline generation systems, the proposed framework combines text and image analysis and delivers a storyline containing textual, pictorial, and structural information to provide a sketch of the topic evolution. A key id...

A graph G is 3-domination-critical (3-critical, for short), if its domination number γ is 3 and the addition of any edge decreases γ by 1. In this paper, we show that every 3-critical graph with independence number 4 and minimum degree 3 is Hamilton-connected. Combining the result with those in [2], [4] and [5], we solve the following conjecture: a connected 3critical graph G is Hamilton-connec...

A subset S of V (G), where G is a simple undirected graph, hop dominating if for each v ∈ (G) \ S, there exists w such that dG(v, w) = 2 and it differentiating N2 G[u] ∩ ̸= G[v] any two distinct vertices u, (G). set ⊆ both in G. The minimum cardinality G, denoted by γdh(G), called the domination number In this paper, we investigate some properties newly defined parameter. particular, characteriz...

The Connected Dominating Set (CDS) principle has emerged as the predominant method for energy-efficient discovery and clustering of power-/location-unaware WSN nodes. While many CDS discovery protocols have been proposed recently, a one-to-one comparative evaluation of these protocols has not been performed on judicious metrics. In this paper, we perform a simulation-based evaluation of three p...

A connected dominating set in a graph is a dominating set of vertices that induces a connected subgraph. We introduce and study the connected-domishold graphs, defined as graphs that admit non-negative real weights associated to their vertices such that a set of vertices is a connected dominating set if and only if the sum of the corresponding weights exceeds a certain threshold. More specifica...