Results 51 to 60 of about 1,529,529 (310)
Triangle-free graphs which are minimal for some nonstable 4-vertex subset
Arab Journal of Mathematical Sciences, 2015 In a graph G, a module is a vertex subset M such that every vertex outside M is adjacent to all or none of M. A graph G is prime if ϕ, the single-vertex sets, and V(G) are the only modules in G.
Mohammad Alzohairi
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Extending Undirected Graph Techniques to Directed Graphs via Category Theory
MathematicsWe use Category Theory to construct a ‘bridge’ relating directed graphs with undirected graphs, such that the notion of direction is preserved. Specifically, we provide an isomorphism between the category of simple directed graphs and a category we call ‘
Sebastian Pardo-Guerra +4 more
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Linear rank-width of distance-hereditary graphs II. Vertex-minor obstructions
, 2017 In the companion paper [Linear rank-width of distance-hereditary graphs I. A polynomial-time algorithm, Algorithmica 78(1):342--377, 2017], we presented a characterization of the linear rank-width of distance-hereditary graphs, from which we derived an ...
Kanté, Mamadou Moustapha, Kwon, O-joung
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Finite prime distance graphs and 2-odd graphs
Discrete Mathematics, 2013 A graph $G$ is a prime distance graph (respectively, a 2-odd graph) if its vertices can be labeled with distinct integers such that for any two adjacent vertices, the difference of their labels is prime (either 2 or odd). We prove that trees, cycles, and bipartite graphs are prime distance graphs, and that Dutch windmill graphs and paper mill graphs ...
Laison, Joshua D. +2 more
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On Minimal Prime Graphs and Posets [PDF]
Order, 2009 We show that there are four infinite prime graphs such that every infinite prime graph with no infinite clique embeds one of these graphs. We derive a similar result for infinite prime posets with no infinite chain or no infinite antichain.
Pouzet, Maurice, Zaguia, Imed
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$H$-product and $H$-threshold graphs
, 2011 This paper is the continuation of the research of the author and his colleagues of the {\it canonical} decomposition of graphs. The idea of the canonical decomposition is to define the binary operation on the set of graphs and to represent the graph ...
Bang-Jensen +26 more
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Exhaustive Enumeration of Spatial Prime Structures
MachinesPrime structures are link chains with 0 DoF (degrees of freedom), not including subchains with 0 or fewer DoF, which are expected to be used in systematic kinematic and dynamic analyses of link mechanisms.
Takahiro Aruga, Nobuyuki Iwatsuki
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Dominating sets and domination polynomials of certain graphs, II [PDF]
Opuscula Mathematica, 2010 The domination polynomial of a graph \(G\) of order \(n\) is the polynomial \(D(G,x) = \sum _{i=\gamma(G)}^n d(G,i)x^i\), where \(d(G,i)\) is the number of dominating sets of \(G\) of size \(i\), and \(\gamma (G)\) is the domination number of \(G\).
Saeid Alikhani, Yee-hock Peng
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A new characterization of the automorphism groups of Mathieu groups
Open Mathematics, 2021 Let cd(G){\rm{cd}}\left(G) be the set of irreducible complex character degrees of a finite group GG. ρ(G)\rho \left(G) denotes the set of primes dividing degrees in cd(G){\rm{cd}}\left(G).
Liu Xin, Chen Guiyun, Yan Yanxiong
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Certain Results on Prime and Prime Distance Labeling of Graphs
Journal of Physics: Conference Series, 2020 Let G be a graph on n vertices. A bijective function f : V (G) → {1, 2,…,n} is said to be a prime labeling if for every e = xy, GCD{f (x),f (y)} = 1. A graph which permits a prime labeling is a “prime graph”.
A. Parthiban, Ajaz Ahmad Pir, A. Felix
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