Results 11 to 20 of about 336,088 (309)
General Properties on Differential Sets of a Graph
Axioms, 2021 Let G=(V,E) be a graph, and let β∈R. Motivated by a service coverage maximization problem with limited resources, we study the β-differential of G. The β-differential of G, denoted by ∂β(G), is defined as ∂β(G):=max{|B(S)|−β|S|suchthatS⊆V}.
Ludwin A. Basilio +3 more
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Independent [1,2]-number versus independent domination number [PDF]
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2017 Abstract A [1; 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and at most two neighbors in it. If the additional requirement that the set be independent is added, the existence of such sets is not guaranteed in every graph.
Aleid, Sahar A. +2 more
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Device-independent quantum random-number generation [PDF]
Nature, 2018 Randomness is critical for many information processing applications, including numerical modeling and cryptography. Device-independent quantum random number generation (DIQRNG) based on the loophole free violation of Bell inequality produces unpredictable genuine randomness without any device assumption and is therefore an ultimate goal in the field of
Liu, Yang +18 more
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Independence Numbers of Johnson-Type Graphs
Bulletin of the Brazilian Mathematical Society, New Series, 2023 We consider a family of distance graphs in $\mathbb{R}^n$ and find its independent numbers in some cases. Define graph $J_{\pm}(n,k,t)$ in the following way: the vertex set consists of all vectors from $\{-1,0,1\}^n$ with $k$ nonzero coordinates; edges connect the pairs of vertices with scalar product $t$.
Cherkashin, Danila, Kiselev, Sergei
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The independence number of circulant triangle-free graphs
AIMS Mathematics, 2020 The independence number of circulant triangle-free graphs for 2-regular, 3-regular graphs are investigated. It is shown that the independence ratio of circulant triangle-free graphs for 3-regular graphs is at least 3/8.
S. Masih Ayat +2 more
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Spanning k-Ended Tree in 2-Connected Graph
Axioms, 2023 Win proved a very famous conclusion that states the graph G with connectivity κ(G), independence number α(G) and α(G)≤κ(G)+k−1(k≥2) contains a spanning k-ended tree. This means that there exists a spanning tree with at most k leaves.
Wanpeng Lei, Jun Yin
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New Bounds for the α-Indices of Graphs
Mathematics, 2020 Let G be a graph, for any real 0≤α≤1, Nikiforov defines the matrix Aα(G) as Aα(G)=αD(G)+(1−α)A(G), where A(G) and D(G) are the adjacency matrix and diagonal matrix of degrees of the vertices of G.
Eber Lenes +2 more
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Independence Number and Disjoint Theta Graphs [PDF]
The Electronic Journal of Combinatorics, 2011 The goal of this paper is to find vertex disjoint even cycles in graphs. For this purpose, define a $\theta$-graph to be a pair of vertices $u, v$ with three internally disjoint paths joining $u$ to $v$. Given an independence number $\alpha$ and a fixed integer $k$, the results contained in this paper provide sharp bounds on the order $f(k, \alpha ...
Fujita, Shinya, Magnant, Colton
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Shor’s bounds for the weighted independence number
Науковий вісник Ужгородського університету. Серія: Математика і інформатика, 2019 Application of a technique of dual Lagrangian quadratic bounds of N.Z. Shor to studying the Maximum Weighted Independent Set problem is described. By the technique, two such N.Z. Shor’s upper bounds are obtained.
П. І. Стецюк +1 more
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On the k-Component Independence Number of a Tree
Discrete Dynamics in Nature and Society, 2021 Let G be a graph and k≥1 be an integer. A subset S of vertices in a graph G is called a k-component independent set of G if each component of GS has order at most k.
Shuting Cheng, Baoyindureng Wu
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