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The difference between the metric dimension and the determining number of a graph
TLDR
We study the maximum value of the difference between the metric dimension and the determining number of a graph as a function of its order. Expand
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Applied Mathematics and Computation Computing the Tutte polynomial of Archimedean tilings
We describe an algorithm to compute the Tutte polynomial of large fragments of Archimedean tilings by squares, triangles, hexagons and combinations thereof. Our algorithm improves a well known methodExpand
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The determining number of Kneser graphs
TLDR
A set of vertices S is a determining set of a graph G if every automorphism of G is uniquely determined by its action on S. Expand
  • 10
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Resolving sets for breaking symmetries of graphs
This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to useExpand
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Distinguishing graphs by their left and right homomorphism profiles
TLDR
We introduce a new property of graphs called 'q-state Potts uniqueness' and relate it to chromatic and Tutte uniqueness, and also to 'chromatic-flow uniqueness', recently studied by Duan, Wu and Yu. Expand
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Stabbers of line segments in the plane
TLDR
The problem of computing a representation of the stabbing lines of a set S of segments in the plane was solved by Edelsbrunner et al. Expand
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Resolving sets for Johnson and Kneser graphs
TLDR
A set of vertices S in a graph G is a resolving set for G if, for any two vertices u,v, there exists [email protected]?S such that the distances d(u,x) d(v,x). Expand
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Tutte Uniqueness of Locally Grid Graphs
TLDR
A graph G is said to be locally grid if the structure around each of its vertices is a 3" 3 rid. Expand
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On the Determining Number and the Metric Dimension of Graphs
TLDR
We provide new proofs and results on the determining number of trees and Cartesian products of graphs and establish some lower bounds on the difference between the two parameters. Expand
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Polynomial graph invariants from homomorphism numbers
TLDR
We give a new method of generating strongly polynomial sequences of graphs, i.e.,?sequences ( H k ) indexed by a tuple k = ( k 1 , ? , k h ) of positive integers, with the property that, for each fixed graph G , the number of homomorphisms from G to H k is given by the evaluation p ( G) . Expand
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