To monitor an electric power system by placing as few phase measurement units (PMUs) as possible is closely related to the famous vertex cover problem and domination problem in graph theory. A set S is a power dominating set (PDS) of a graph G = (V,E), if every vertex and every edge in the system is observed following the observation rules of power system monitoring. The minimum cardinality of ...

For a graph G and a positive integer k, the k-power of G is the graph G with V (G) as its vertex set and {(u, v)|u, v ∈ V (G), dG(u, v) ≤ k} as its edge set where dG(u, v) is the distance between u and v in graph G. The k-Steiner root problem on a graph G asks for a tree T with V (G) ⊆ V (T ) and G is the subgraph of T k induced by V (G). If such a tree T exists, we call it a k-Steiner root of ...

Single labeled biometric recognition is one of the main challenges to graph-based transductive classification learning. To enhance the recognition rate of single labeled problem, sparse representation provides a feasible strategy for representation learning. In this paper, we developed a power l1-graph learning technique for semi-supervised learning, called label propagation by power l1-graph (...

Connectivity in wireless ad hoc and sensor networks is typically analyzed using a graph-theoretic approach. In this paper, we investigate an alternative communication-theoretic approach for determining the minimum transmit power required for achieving connectivity. Our results show that, if there is significant multipath fading and/or multiple access interference in the network, then graph-theo...

In this paper the web is analyzed as a graph aggregated by host and pay-level domain (PLD). The web graph datasets, publicly available, have been released by the Common Crawl Foundation 1 and are based on a web crawl performed during the period May-June-July 2017. The host graph has ∼1.3 billion nodes and ∼5.3 billion arcs. The PLD graph has ∼91 million nodes and ∼1.1 billion arcs. We study the...

Task graph scheduling is a multi-objective optimization and NP-hard problem. In this paper a new algorithm on homogeneous multiprocessors systems is proposed. Basically, scheduling algorithms are targeted to balance the two parameters of time and energy consumption. These two parameters are up to a certain limit in contrast with each other and improvement of one causes reduction in the othe...

The webgraph is the graph generated from the link structure of the web pages. In this graph, each node represents a web page and each edge is a hyperlink from one page to another. The webgraph has a particular structure, that is not similar to other known graphs, and it grows continuously. Nowadays it contains more then 25 billion nodes and about 400 billion edges. Even some properties of this ...

A graph G that has a perfect matching is n-extendable if every matching of size n lies in a perfect matching of G. We show that when the connectivity of a line graph, power graph, or total graph is sufficiently large then it is n-extendable. Specifically: if G has even size and is (2n + 1)edge-connected or (n + 2)-connected, then its line graph is n-extendable; if G has even order and is (n + 1...

We determine the list chromatic number of the square of a graph χl(G 2) in terms of its maximum degree ∆ when its maximum average degree, denoted mad(G), is sufficiently small. For ∆ ≥ 6, if mad(G) < 2 + 4∆−8 5∆+2 , then χl(G 2) = ∆ + 1. In particular, if G is planar with girth g ≥ 7 + 12 ∆−2 , then χl(G 2) = ∆ + 1. Under the same conditions, χil(G) = ∆, where χ i l is the list injective chroma...

A vertex coloring of a graph G is a multiset coloring if the multisets of colors of the neighbors of every two adjacent vertices are different. The minimum k for which G has a multiset k-coloring is the multiset chromatic number χm(G) of G. For every graph G, χm(G) is bounded above by its chromatic number χ(G). The multiset chromatic number is determined for every complete multipartite graph as...