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pro vyhledávání: '"Beaton, Iain"'
Autor:
Beaton, Iain, Cameron, Ben
A graph $G$ is $k$-vertex-critical if $\chi(G)=k$ but $\chi(G-v)
Externí odkaz:
http://arxiv.org/abs/2408.05027
Autor:
Beaton, Iain, Cameron, Ben
In this paper we study the the average order of dominating sets in a graph, $\operatorname{avd}(G)$. Like other average graph parameters, the extremal graphs are of interest. Beaton and Brown (2021) conjectured that for all graphs $G$ of order $n$ wi
Externí odkaz:
http://arxiv.org/abs/2208.10475
Autor:
Beaton, Iain, Brown, Jason I.
A dominating set $S$ of a graph $G$ of order $n$ is a subset of the vertices of $G$ such that every vertex is either in $S$ or adjacent to a vertex of $S$. The domination polynomial is defined by $D(G,x) = \sum d_k x^k$ where $d_k$ is the number of d
Externí odkaz:
http://arxiv.org/abs/2012.15193
Autor:
Beaton, Iain, Brown, Jason I.
A polynomial is said to be unimodal if its coefficients are non-decreasing and then non-increasing. The domination polynomial of a graph $G$ is the generating function of the number of domination sets of each cardinality in $G$, and its coefficients
Externí odkaz:
http://arxiv.org/abs/2012.11813
Autor:
Beaton, Iain, Brown, Jason I.
This papers focuses on the average order of dominating sets of a graph. We find the extremal graphs for the maximum and minimum value over all graphs on $n$ vertices, while for trees we prove that the star minimizes the average order of dominating se
Externí odkaz:
http://arxiv.org/abs/2008.06531
Autor:
Beaton, Iain, Cameron, Ben
The independence polynomial of a graph $G$, denoted $I(G,x)$, is the generating polynomial for the number of independent sets of each size. The roots of $I(G,x)$ are called the \textit{independence roots} of $G$. It is known that for every graph $G$,
Externí odkaz:
http://arxiv.org/abs/2006.05511
Akademický článek
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The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size. Two graphs are said to be \textit{independence equivalent} if they have equivalent independence polynomials. We extend previous work
Externí odkaz:
http://arxiv.org/abs/1810.05317
Autor:
Beaton, Iain, Brown, Jason I.
A dominating set $S$ of a graph $G$ of order $n$ is a subset of the vertices of $G$ such that every vertex is either in $S$ or adjacent to a vertex of $S$. %The domination number $G$, denoted $\gamma (G)$, is the cardinality of the smallest dominatin
Externí odkaz:
http://arxiv.org/abs/1710.03871
