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The impact of Parkinson's disease on striatal network connectivity and corticostriatal drive: An in silico study. [PDF]

open access: yesNetw Neurosci
Carannante I   +8 more
europepmc   +1 more source

Clique Chromatic Numbers of Intersection Graphs

Mathematical Notes, 2019
The clique chromatic number \(\chi_c(G)\) of a graph \(G\) is the minimum \(k\) for which there exists a \(k\)-coloring of the vertices of \(G\) such that all inclusion-maximal cliques, except for isolated vertices, are non-monochromatic. When \([n]=\{1,2,\dots,n\}\), \(G(n,r,s)\) is the graph whose vertex-set is \(\binom{[n]}{r}\), and whose edges ...
Zakharov, D. A., Raigorodskii, A. M.
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Clique-transversal number of graphs whose clique-graphs are trees

Journal of Shanghai University (English Edition), 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liang, Zuosong, Shan, Erfang
openaire   +2 more sources

Independence number and clique minors

Journal of Graph Theory, 2007
AbstractThe Hadwiger number ${h}({G})$ of a graph G is the maximum integer t such that ${K}_{t}$ is a minor of G. Since $\chi({G})\cdot\alpha({G})\geq |{G}|$, Hadwiger's conjecture implies that ${h}({G})\cdot \alpha({G})\geq |{G}|$, where $\alpha({G})$ and $|{G}|$ denote the independence number and the number of vertices of G, respectively.
Kawarabayashi, Ken Ichi, Song, Zi Xia
openaire   +2 more sources

The Clique Numbers of Regular Graphs

Graphs and Combinatorics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Relative Clique Number of Planar Signed Graphs

Discrete Applied Mathematics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Das, Sandip   +3 more
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CLIQUE NUMBERS OF PALEY GRAPHS

Quaestiones Mathematicae, 1988
Abstract The clique number of the Paley graph G(q), where q, is a prime power with q ≡ 1 (mod 4) is known to be Jq, when q, is a square. When q, is a non-square the problem of finding a formula for the clique number seems to be a hard one although its value has been obtained by computer search for prime values of q, satisfying 5 ⋚ q, ⋚ 1601.
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On Cliques and Clique Chromatic Numbers in Line, Lict and Lictact Graphs

2020
The line graph of a graph G denoted as L(G) has vertex set E(G) in which two vertices are adjacent if they correspond to adjacent edges in G. The lict graph and litact graph of G, denoted as \(L_c(G)\) and \(L_{ct}(G)\), respectively having vertex set \(E(G)\cup C(G)\) (here C(G) is the set of cut-vertices of G), two of these vertices will be adjacent ...
Rashmi Jain, Anuj Kumar Jain
openaire   +1 more source

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