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Infinite Numbers of Infinite Classes L-Borderenergetic Graphs
Match - Communications in Mathematical and in Computer Chemistry, 2023The graph G of order n is an L-borderenergetic graph which means it has the same Laplacian energy as the complete graph Kn. In this paper, we find that the combination of complete bipartite graphs and stars can construct infinite numbers of infinite classes L-borderenergetic graphs.
Li, Qiuping, Tang, Liangwen
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2021
In this chapter we extend the theory of the key concepts introduced in the previous chapter. In particular, we collect various tools that are needed at later parts of the book and provide further conceptual insights.
Matthias Keller +2 more
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In this chapter we extend the theory of the key concepts introduced in the previous chapter. In particular, we collect various tools that are needed at later parts of the book and provide further conceptual insights.
Matthias Keller +2 more
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Results in Mathematics, 1996
Let \(\Phi\) be any graph-valued function (a simple example is the well-known function \({\mathcal L}: G\to {\mathcal L}G\) which arranges to every graph \(G\) its line graph \({\mathcal L}G\)). A graph \(G\) is \(\Phi\)-periodic if there is an integer \(p>0\) such that \(G\) and \(\Phi^pG\) are isomorphic. A graph \(G\) is \(\Phi\)-fixed if \(G\) and \
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Let \(\Phi\) be any graph-valued function (a simple example is the well-known function \({\mathcal L}: G\to {\mathcal L}G\) which arranges to every graph \(G\) its line graph \({\mathcal L}G\)). A graph \(G\) is \(\Phi\)-periodic if there is an integer \(p>0\) such that \(G\) and \(\Phi^pG\) are isomorphic. A graph \(G\) is \(\Phi\)-fixed if \(G\) and \
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Doklady Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kostenko, Aleksey +3 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kostenko, Aleksey +3 more
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Essentially Infinite Colourings of Graphs
Journal of the London Mathematical Society, 2000A coloring of edges of a complete graph \(K_n\) is \((k,\varepsilon)\)-bounded if there is a set \(S\) of at most \(k\) colors such that all but at most \(\varepsilon \choose{n}{2}\) edges are colored with colors from \(S\).
Bollobás, B. +2 more
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Infinite Sets and Infinite Graphs
1985E.C. MILNER: Let me begin with a problem due to Prikry and myself. First I’ll state a theorem concerning the depth of an ordered set. The depth of a partial order is the least ordinal γ such that does not embed γ*, the reverse of γ. For example vK has depth v+, if v ⪰ ω, κ ⪰ 2.
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On highly ramsey infinite graphs
Journal of Graph Theory, 2008AbstractWe show that, for r ≥ 2 and k ≥ 3, there exists a positive constant c such that for large enough n there are 2 non‐isomorphic graphs on at most n vertices that are r‐ramsey‐minimal for the odd cycle C2k+1. © 2008 Wiley Periodicals, Inc.
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Nevanlinna Theory on Infinite Graphs
Computational Methods and Function TheoryzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Atsuji, Atsushi, Kaneko, Hiroshi
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1990
Given a graph \(G\), a covering of \(G\) is a set of subgraphs \(\{G_ 1,G_ 2,\dots,G_ k\}\) such that every edge of \(G\) is in some \(G_ i\). A set of edges \(\{e_ 1,e_ 2,\dots,e_ k\}\) with \(e_ i\in E(G_ i)\) is called a set of distinct representing edges. \textit{L.
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Given a graph \(G\), a covering of \(G\) is a set of subgraphs \(\{G_ 1,G_ 2,\dots,G_ k\}\) such that every edge of \(G\) is in some \(G_ i\). A set of edges \(\{e_ 1,e_ 2,\dots,e_ k\}\) with \(e_ i\in E(G_ i)\) is called a set of distinct representing edges. \textit{L.
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