Interpreting Node Embedding with Text-labeled Graphs

For a non-empty ground set [Formula: see text], finite or infinite, the set-valuation or set-labeling of a given graph [Formula: see text] is an injective function [Formula: see text], where [Formula: see text] is the power set of the set [Formula: see text]. A set-valuation or a set-labeling of a graph [Formula: see text] is an injective set-valued function [Formula: see text] such that the induced function [Formula: see text] is defined by [Formula: see text] for every [Formula: see text], where [Formula: see text] is a binary operation on sets. Let [Formula: see text] be the set of all non-negative integers and [Formula: see text] be its power set. An integer additive set-labeling (IASL) is defined as an injective function [Formula: see text] such that the induced function [Formula: see text] is defined by [Formula: see text]. An IASL [Formula: see text] is said to be an integer additive set-indexer if [Formula: see text] is also injective. A weak IASL is an IASL [Formula: see text] such that [Formula: see text]. In this paper, critical and creative review of certain studies made on the concepts and properties of weak integer additive set-valued graphs is intended.

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Enumerating the Number of Connected Vertices Labeled Graph of Order Six with Maximum Ten Loops and Containing No Parallel Edges

Science & Technology Indonesia ◽

10.26554/sti.2020.5.4.131-135 ◽

2020 ◽

Vol 5 (4) ◽

pp. 131

Author(s):

Wamiliana Wamiliana ◽

Amanto Amanto ◽

Mustofa Usman ◽

Muslim Ansori ◽

Fadila Cahya Puri

Keyword(s):

Connected Graph ◽

Labeled Graph ◽

Labeled Graphs

A Graph G (V, E) is said to be a connected graph if for every two vertices on the graph there exist at least a path connecting them, otherwise, the graph is disconnected. Two edges or more that connect the same pair of vertices are called parallel edges, and an edge that starts and ends at the same vertex is called a loop. A graph is called simple if it containing no loops nor parallel edges. Given n vertices and m edges, m ≥ 1, there are many graphs that can be formed, either connected or disconnected. In this research, we will discuss how to calculate the number of connected vertices labeled graphs of order six (isomorphism graphs are counted as one), with a maximum loop of ten without parallel edges.

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Bisimulations on Data Graphs

Journal of Artificial Intelligence Research ◽

10.1613/jair.5637 ◽

2018 ◽

Vol 61 ◽

pp. 171-213 ◽

Cited By ~ 1

Author(s):

Sergio Abriola ◽

Pablo Barceló ◽

Diego Figueira ◽

Santiago Figueira

Keyword(s):

Constraint Satisfaction ◽

Transitive Closure ◽

Modal Logics ◽

Closure Operators ◽

External Observer ◽

Complexity Bounds ◽

Fundamental Notion ◽

Labeled Graphs ◽

Non Locality

Bisimulation provides structural conditions to characterize indistinguishability from an external observer between nodes on labeled graphs. It is a fundamental notion used in many areas, such as verification, graph-structured databases, and constraint satisfaction. However, several current applications use graphs where nodes also contain data (the so called "data graphs"), and where observers can test for equality or inequality of data values (e.g., asking the attribute 'name' of a node to be different from that of all its neighbors). The present work constitutes a first investigation of "data aware" bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational indistinguishability for XPath ---a language that extends modal logics like PDL with tests for data equality--- with and without transitive closure operators. We show that in general the problem is PSpace-complete, but identify several restrictions that yield better complexity bounds (coNP, PTime) by controlling suitable parameters of the problem, namely the amount of non-locality allowed, and the class of models considered (graphs, DAGs, trees). In particular, this analysis yields a hierarchy of tractable fragments.

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Simple Reductions from Formula-SAT to Pattern Matching on Labeled Graphs and Subtree Isomorphism

Symposium on Simplicity in Algorithms (SOSA) ◽

10.1137/1.9781611976496.26 ◽

2021 ◽

pp. 232-242

Author(s):

Daniel Gibney ◽

Gary Hoppenworth ◽

Sharma V. Thankachan

Keyword(s):

Pattern Matching ◽

Labeled Graphs ◽

Subtree Isomorphism

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Some properties of a dissimilarity measure for labeled graphs

Publications Mathématiques de Besançon ◽

10.5802/pmb.o-7 ◽

2016 ◽

pp. 85-94

Author(s):

Nicolas Wicker ◽

Canh Hao Nguyen ◽

Hiroshi Mamitsuka

Keyword(s):

Dissimilarity Measure ◽

Labeled Graphs

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Construction and pure infiniteness of $C^*$-algebras associated with lambda-graph systems

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-14964 ◽

2005 ◽

Vol 97 (1) ◽

pp. 73 ◽

Cited By ~ 8

Author(s):

Kengo Matsumoto

Keyword(s):

Hilbert Space ◽

Bratteli Diagram ◽

C Algebra ◽

C Algebras ◽

Shift Transformation ◽

Labeled Graphs ◽

Graph System ◽

Creation Operators

A $\lambda$-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. In [16] the author has introduced a $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ associated with a $\lambda$-graph system $\mathfrak{L}$ by using groupoid method as a generalization of the Cuntz-Krieger algebras. In this paper, we concretely construct the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ by using both creation operators and projections on a sub Fock Hilbert space associated with $\mathfrak{L}$. We also introduce a new irreducible condition on $\mathfrak{L}$ under which the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ becomes simple and purely infinite.

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