Results 81 to 90 of about 1,022,735 (236)
Independent Roman Domination Stable and Vertex-Critical Graphs
IEEE Access, 2018 A Roman dominating function (RDF) on a graph $G$ is a function $f: V(G) \rightarrow \{0, 1, 2\}$ for which every vertex assigned 0 is adjacent to a vertex assigned 2. The weight of an RDF is the value $\omega (f) = \sum _{u \in V(G)}f(u)$ .
Pu Wu +5 more
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, 2007 Recently, it has been shown that, when the dimension of a graph turns out to be infinite dimensional in a broad sense, the upper critical surface and the corresponding critical behavior of an arbitrary Ising spin glass model defined over such a graph ...
Baxter R J +13 more
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Exponent-critical primitive graphs and the Kronecker product
Electronic Journal of Graph Theory and Applications, 2019 A directed graph is primitive of exponent t if it contains walks of length t between all pairs of vertices, and t is minimal with this property. Moreover, it is exponent-critical if the deletion of any arc results in an imprimitive graph or in a ...
Olga O'Mahony, Rachel Quinlan
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A Note on Near-factor-critical Graphs [PDF]
, 2014 A near-factor of a finite simple graph $G$ is a matching that saturates all vertices except one. A graph $G$ is said to be near-factor-critical if the deletion of any vertex from $G$ results in a subgraph that has a near-factor. We prove that a connected
Huang, Kuo-Ching, Lih, Ko-Wei
core
Critical percolation on certain non-unimodular graphs [PDF]
, 2005 An important conjecture in percolation theory is that almost surely no infinite cluster exists in critical percolation on any transitive graph for which the critical probability is less than 1. Earlier work has established this for the amenable cases Z^2
Peres, Yuval +2 more
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Mixing time of near-critical random graphs
, 2012 Let $\mathcal{C}_1$ be the largest component of the Erd\H{o}s--R\'{e}nyi random graph $\mathcal{G}(n,p)$. The mixing time of random walk on $\mathcal {C}_1$ in the strictly supercritical regime, $p=c/n$ with fixed $c>1$, was shown to have order $\log^2n$
Ding, Jian, Lubetzky, Eyal, Peres, Yuval
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New Results on Minimal Strongly Imperfect Graphs [PDF]
Scientific Annals of Computer Science, 2008 The characterization of strongly perfect graphs by a restricted list of forbidden induced subgraphs has remained an open question for a long time. The minimal strongly imperfect graphs which are simultaneous imperfect are only odd holes and odd antiholes
V. Anastasoaei, E. Olaru
doaj
Cyclic Critical Groups of Graphs
, 2016 In this note, we describe a construction that leads to families of graphs whose critical groups are cyclic. For some of these families we are able to give a formula for the number of spanning trees of the graph, which then determines the group ...
Becker, Ryan P., Glass, Darren B.
core
Factor-Critical Property in 3-Dominating-Critical Graphs
, 2006 A vertex subset $S$ of a graph $G$ is a dominating set if every vertex of $G$ either belongs to $S$ or is adjacent to a vertex of $S$. The cardinality of a smallest dominating set is called the dominating number of $G$ and is denoted by $\gamma(G)$.
Wang, Tao, Yu, Qinglin
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Quadratic maps with a periodic critical point of period 2 [PDF]
, 2015 We provide a complete classification of possible graphs of rational preperiodic points of endomorphisms of the projective line of degree 2 defined over the rationals with a rational periodic critical point of period 2, under the assumption that these ...
Canci, J. K., Vishkautsan, Solomon
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