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Graphs whose vertex set can be partitioned into a total dominating set and an independent dominating set [PDF]
Opuscula MathematicaA graph \(G\) whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. We give constructions that yield infinite families of graphs that are TI-graphs, as well as constructions that yield ...
Teresa W. Haynes, Michael A. Henning
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On the Factorization of Graphs with Exactly One Vertex of Infinite Degree [PDF]
, 1983 We give a necessary and sufficient condition for the existence of a 1-factor in graphs with exactly one vertex of infinite ...
Bry, François
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Cutsets in Infinite Graphs [PDF]
Combinatorics, Probability and Computing, 2006 We answer three questions posed in a paper by Babson and Benjamini. They introduced a parameter $C_G$ for Cayley graphs $G$ that has significant application to percolation. For a minimal cutset of $G$ and a partition of this cutset into two classes, take the minimal distance between the two classes.
openaire +2 more sources
Seidel Integral Complete Split Graphs [PDF]
Mathematics Interdisciplinary Research, 2019 In the paper we consider a generalized join operation, that is, the H-join on graphs where H is an arbitrary graph. In terms of Seidel matrix of graphs we determine the Seidel spectrum of the graphs obtained by this operation on regular graphs.
Pavel Hic +2 more
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Spectral Theory of Infinite Quantum Graphs [PDF]
, 2018 We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a close connection
Kostenko, Aleksey +4 more
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Infinite families of asymmetric graphs
AKCE International Journal of Graphs and Combinatorics, 2020 A graph G is asymmetric if its automorphism group of vertices is trivial. Asymmetric graphs were introduced by Erdős and Rényi in 1963. They showed that the probability of a graph on n vertices being asymmetric tends to 1 as n tends to infinity.
Alejandra Brewer +5 more
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Duality of infinite graphs [PDF]
, 1982 Some basic results on duality of infinite graphs are established and it is proven that a block has a dual graph if and only if it is planar and any two vertices are separated by a finite edge cut.
Thomassen, Carsten
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Characterising memory in infinite games [PDF]
Logical Methods in Computer ScienceThis paper is concerned with games of infinite duration played over potentially infinite graphs. Recently, Ohlmann (LICS 2022) presented a characterisation of objectives admitting optimal positional strategies, by means of universal graphs: an objective ...
Antonio Casares, Pierre Ohlmann
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On external presentations of infinite graphs [PDF]
Electronic Proceedings in Theoretical Computer Science, 2009 The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices.
Christophe Morvan
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On Transmission Irregular Cubic Graphs of an Arbitrary Order
Mathematics, 2022 The transmission of a vertex v of a graph G is the sum of distances from v to all the other vertices of G. A transmission irregular graph (TI graph) has mutually distinct vertex transmissions.
Anatoly Yu. Bezhaev, Andrey A. Dobrynin
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