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Fault Tolerant Detectors for Distinguishing Sets in Graphs

Suk J. Seo, Peter J. Slater (2015)

Discussiones Mathematicae Graph Theory

For various domination-related parameters involving locating devices (distinguishing sets) that function as places from which detectors can determine information about the location of an “intruder”, several types of possible detector faults are identified. Two of these fault tolerant detector types for distinguishing sets are considered here, namely redundant distinguishing and detection distinguishing. Illustrating these concepts, we focus primarily on open-locating-dominating sets.

Fiedler vectors with unbalanced sign patterns

Sooyeong Kim, Stephen J. Kirkland (2021)

Czechoslovak Mathematical Journal

In spectral bisection, a Fielder vector is used for partitioning a graph into two connected subgraphs according to its sign pattern. We investigate graphs having Fiedler vectors with unbalanced sign patterns such that a partition can result in two connected subgraphs that are distinctly different in size. We present a characterization of graphs having a Fiedler vector with exactly one negative component, and discuss some classes of such graphs. We also establish an analogous result for regular graphs...

Finding H -partitions efficiently

Simone Dantas, Celina M. H. de Figueiredo, Sylvain Gravier, Sulamita Klein (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We study the concept of an H -partition of the vertex set of a graph G , which includes all vertex partitioning problems into four parts which we require to be nonempty with only external constraints according to the structure of a model graph H , with the exception of two cases, one that has already been classified as polynomial, and the other one remains unclassified. In the context of more general vertex-partition problems, the problems addressed in this paper have these properties: non-list, 4 -part,...

Finding H-partitions efficiently

Simone Dantas, Celina M.H. de Figueiredo, Sylvain Gravier, Sulamita Klein (2010)

RAIRO - Theoretical Informatics and Applications

We study the concept of an H-partition of the vertex set of a graph G, which includes all vertex partitioning problems into four parts which we require to be nonempty with only external constraints according to the structure of a model graph H, with the exception of two cases, one that has already been classified as polynomial, and the other one remains unclassified. In the context of more general vertex-partition problems, the problems addressed in this paper have these properties: non-list, 4-part, external...

Finding vertex-disjoint cycle cover of undirected graph using the least-squares method

Lamač, Jan, Vlasák, Miloslav (2023)

Programs and Algorithms of Numerical Mathematics

We investigate the properties of the least-squares solution of the system of equations with a matrix being the incidence matrix of a given undirected connected graph G and we propose an algorithm that uses this solution for finding a vertex-disjoint cycle cover (2-factor) of the graph G .

Finite canonization

Saharon Shelah (1996)

Commentationes Mathematicae Universitatis Carolinae

The canonization theorem says that for given m , n for some m * (the first one is called E R ( n ; m ) ) we have for every function f with domain [ 1 , ⋯ , m * ] n , for some A ∈ [ 1 , ⋯ , m * ] m , the question of when the equality f ( i 1 , ⋯ , i n ) = f ( j 1 , ⋯ , j n ) (where i 1 < ⋯ < i n and j 1 < ⋯ j n are from A ) holds has the simplest answer: for some v ⊆ { 1 , ⋯ , n } the equality holds iff ⋀ ℓ ∈ v i ℓ = j ℓ . We improve the bound on E R ( n , m ) so that fixing n the number of exponentiation needed to calculate E R ( n , m ) is best possible.

Finite nondense point set analysis

Jozef Zámožík, Mária Mišútová (1993)

Applications of Mathematics

The paper deals with the decomposition and with the boundarz and hull construction of the so-called nondense point set. This problem and its applications have been frequently studied in computational geometry, raster graphics and, in particular, in the image processing (see e.g. [3], [6], [7], [8], [9], [10]). We solve a problem of the point set decomposition by means of certain relations in graph theory.

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