The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known vertex covering and dominating set problems in graphs (see [T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, M.A. Henning, Power domination in graphs applied to electrical power networks, SIAM J. Discrete Math. 15(4) (2002) 519–529]). A set S of v...

In this paper, we continue the study of power domination in graphs (see SIAM J. Discrete Math. 15 (2002), 519–529; SIAM J. Discrete Math. 22 (2008), 554–567; SIAM J. Discrete Math. 23 (2009), 1382–1399). Power domination in graphs was birthed from the problem of monitoring an electric power system by placing as few measurement devices in the system as possible. A set of vertices is defined to b...

Large graphs abound around us – online social networks, Web graphs, the Internet, citation networks, protein interaction networks, telephone call graphs, peer-to-peer overlay networks, electric power grid networks, etc. Many reallife graphs are power-law graphs. A fundamental challenge in today’s Big Data world is storage and processing of these large-scale power-law graphs. In this thesis, we ...

Graph Logic, a query language being a sublogic of Monadic Second Order Logic is studied in [CGG02]. In the paper [DGG04] the expressiveness power of Graph Logic is examined, and it is shown, for many MSO properties, how to express them in Graph Logic. But despite of the positive examples, it is conjectured there that Graph Logic is strictly less expressive than MSO Logic. Here we give a proof o...

Networks play a crucial role in computational biology, yet their analysis and representation is still an open problem. Power Graph Analysis is a lossless transformation of biological networks into a compact, less redundant representation, exploiting the abundance of cliques and bicliques as elementary topological motifs. We demonstrate with five examples the advantages of Power Graph Analysis. ...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

For the-IBM PC or compatible personal computer with 512K memory, enhanced graphics adapter (EGA) color graphics card with 256K memory, one floppy disk drive and a hard disk, DOS version 2.0 or later, CRT display compatible with the EGA card, and a parallel printer with graphics capability. $395.00. Boeing Graph is a program for creating full-color business and scientific graphs. The program des...

CIM/E is an easy and efficient electric power model exchange standard between different Energy Management System vendors. With the rapid growth of data size and system complexity, the traditional relational database is not the best option to store and process the data. In contrast, the graph database and graph computation show their potential advantages to handle the power system data and perfo...

For any positive integer s, a [2, 2s]-factor in a graph G is a connected even factor with maximum degree at most 2s. We prove that if every induced S(K1,2s+1) in a graph G has at least 3 edges in a block of degree at most two, then G has a [2, 2s]-factor. This extends the results of Hendry and Vogler and of Abderrezzak et al.