Results 21 to 30 of about 1,307,438 (325)
Powers of chordal graphs [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1983 AbstractAn undirected simple graph G is called chordal if every circle of G of length greater than 3 has a chord. For a chordal graph G, we prove the following: (i) If m is an odd positive integer, Gm is chordal. (ii) If m is an even positive integer and if Gm is not chordal, then none of the edges of any chordless cycle of Gm is an edge of Gr, r < ...
R. Balakrishnan, P. Paulraja
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Power Domination in the Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2020 The problem of monitoring an electric power system by placing as few measurement devices in the system can be formulated as a power dominating set problem in graph theory.
Zhao Min, Shan Erfang, Kang Liying
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Power Domination Number On Shackle Operation with Points as Lingkage
JTAM (Jurnal Teori dan Aplikasi Matematika), 2020 The Power dominating set is a minimum point of determination in a graph that can dominate the connected dots around it, with a minimum domination point.
Ilham Saifudin
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A survey on the development status and application prospects of knowledge graph in smart grids
IET Generation, Transmission & Distribution, 2021 With the advent of the electric power big data era, semantic interoperability and interconnection of power data have received extensive attention. Knowledge graph technology is a new method describing the complex relationships between concepts and ...
Jian Wang, Xi Wang, Chaoqun Ma, Lei Kou
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Mode Entanglement and Entangling power in Bosonic Graphs [PDF]
, 2003 We analyze the quantum entanglement properties of bosonic particles hopping over graph structures.Mode-entanglement of a graph vertex with respect the rest of the graph is generated, starting from a product state, by turning on for a finite time a ...
Giorda, Paolo, Zanardi, Paolo
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The Electronic Journal of Combinatorics, 2011 For a graph $G$, its $r$th power is constructed by placing an edge between two vertices if they are within distance $r$ of each other. In this note we study the amount of edges added to a graph by taking its $r$th power. In particular we obtain that, for $r\geq 3$, either the $r$th power is complete or "many" new edges are added.
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Regularity of bicyclic graphs and their powers [PDF]
Journal of Algebra and Its Applications, 2019 Let [Formula: see text] be the edge ideal of a bicyclic graph [Formula: see text] with a dumbbell as the base graph. In this paper, we characterize the Castelnuovo–Mumford regularity of [Formula: see text] in terms of the induced matching number of [Formula: see text]. For the base case of this family of graphs, i.e.
Sepehr Jafari +4 more
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The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph.
Evi Yuniartika Asmarani +5 more
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Improved Optimal and Approximate Power Graph Compression for Clearer Visualisation of Dense Graphs [PDF]
, 2013 Drawings of highly connected (dense) graphs can be very difficult to read. Power Graph Analysis offers an alternate way to draw a graph in which sets of nodes with common neighbours are shown grouped into modules.
Dwyer, Tim +5 more
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The power graph of a torsion-free group determines the directed power graph [PDF]
Discrete Applied Mathematics, 2021 The directed power graph $\vec{\mathcal G}(\mathbf G)$ of a group $\mathbf G$ is the simple digraph with vertex set $G$ such that $x\rightarrow y$ if $y$ is a power of $x$. The power graph of $\mathbf G$, denoted with $\mathcal G(\mathbf G)$, is the underlying simple graph. In this paper, for groups $\mathbf G$ and $\mathbf H$, the following is proved.
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