Results 31 to 40 of about 3,157 (213)
On the Structure of the Power Graph and the Enhanced Power Graph of a Group
The Electronic Journal of Combinatorics, 2017 Let $G$ be a group. The power graph of $G$ is a graph with the vertex set $G$, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence number. For a bounded exponent group, we prove its power graph is a perfect graph and we determine its clique ...
Ghodratollah Aalipour +4 more
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Power graphs and exchange property for resolving sets
Open Mathematics, 2019 Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given.
Abbas Ghulam +4 more
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Graphs and Combinatorics, 2017 The {\em power index} $Θ(Γ)$ of a graph $Γ$ is the least order of a group $G$ such that $Γ$ can embed into the power graph of $G$. Furthermore, this group $G$ is {\em $Γ$-optimal} if $G$ has order $Θ(Γ)$. We say that $Γ$ is {\em power-critical} if its order equals to $Θ(Γ)$. This paper focuses on the power indices of complete graphs, complete bipartite
Xuanlong Ma, Min Feng 0004, Kaishun Wang
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Connectivity of 2-distance graphs [PDF]
Journal of Mahani Mathematical ResearchFor a simple graph $G$, the $2$-distance graph, $D_2(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if their distance is $2$ in the graph $G$. In this paper, we characterize all graphs with connected $2$-distance graphs.
Sayyed Heidar Jafari, Seyed Reza Musawi
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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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A Random Graph Model for Power Law Graphs [PDF]
Experimental Mathematics, 2001 We propose a random graph model which is a special case of sparserandom graphs with given degree sequences which satisfy a power law. This model involves only a small number of paramo eters, called logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. From these parameters, various properties of the
Aiello, William, Chung, Fan, Lu, Linyuan
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Graph Powering and Spectral Robustness
SIAM Journal on Mathematics of Data Science, 2020 Spectral algorithms, such as principal component analysis and spectral clustering, typically require careful data transformations to be effective: upon observing a matrix $A$, one may look at the spectrum of $ψ(A)$ for a properly chosen $ψ$. The issue is that the spectrum of $A$ might be contaminated by non-informational top eigenvalues, e.g., due to ...
Abbe, Emmanuel +3 more
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Quotient graphs for power graphs [PDF]
Rendiconti del Seminario Matematico della Università di Padova, 2017 In a previous paper of the first author a procedure was developed for counting the components of a graph through the knowledge of the components of one of its quotient graphs. Here we apply that procedure to the proper power graph \mathcal{P}_0(G ...
BUBBOLONI, DANIELA +2 more
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The cubic power graph of finite abelian groups
AKCE International Journal of Graphs and Combinatorics, 2021 Let G be a finite abelian group with identity 0. For an integer the additive power graph of G is the simple undirected graph with vertex set G in which two distinct vertices x and y are adjacent if and only if x + y = nt for some with When the additive ...
R. Raveendra Prathap, T. Tamizh Chelvam
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Clawfreeness of the powers of a graph
Discrete Applied Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Patrick Bahls, Nicole A. Gin
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