On Incidence Matrices of X-Labeled Graphs

2018 ◽  
Vol 5 (1) ◽  
pp. 18-28
Author(s):  
Wadhah S. Jassim ◽  
Farman Mohammad
Keyword(s):  
Incidence Matrices ◽  
Labeled Graphs

scholarly journals Incidence Matrices of X-Labled Graphs and an Application

2009 ◽  
Vol 14 ◽  
pp. 61
Author(s):  
W.S. Jassim
Keyword(s):  
Computer Program ◽  
Directed Graph ◽  
Incidence Matrices ◽  
Labeled Graphs ◽  
Definition Of

In this work, we have made some modifications on the definition of the incidence matrices of a directed graph, to let the incidence matrices to be   more  confident for X – Labeled graphs.  The new incidence matrices are called  the incidence matrices of  X – Labeled graphs, and  we used the new definition to give a computer program for Nickolas`s Algorithm .  

scholarly journals Materials property prediction using symmetry-labeled graphs as atomic position independent descriptors

2019 ◽  
Vol 100 (10) ◽  
Author(s):  
Peter Bjørn Jørgensen ◽  
Estefanía Garijo del Río ◽  
Mikkel N. Schmidt ◽  
Karsten Wedel Jacobsen
Keyword(s):  
Atomic Position ◽  
Property Prediction ◽  
Labeled Graphs

scholarly journals Weak integer additive set-labeled graphs: A creative review

2015 ◽  
Vol 08 (03) ◽  
pp. 1550052 ◽  
Author(s):  
N. K. Sudev ◽  
K. A. Germina ◽  
K. P. Chithra
Keyword(s):  
Binary Operation ◽  
Labeled Graphs ◽  
Injective Function ◽  
Power Set

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.

scholarly journals Maximal Arcs, Codes, and New Links Between Projective Planes of Order 16

10.37236/9008 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Mustafa Gezek ◽  
Rudi Mathon ◽  
Vladimir D. Tonchev
Keyword(s):  
Minimum Distance ◽  
Linear Codes ◽  
Projective Planes ◽  
Upper And Lower Bounds ◽  
Dual Codes ◽  
Binary Linear Codes ◽  
Incidence Matrices ◽  
Maximal Arc ◽  
Maximal Arcs ◽  
Even Order

In this paper we consider binary linear codes spanned by incidence matrices of Steiner 2-designs associated with maximal arcs in projective planes of even order, and their dual codes. Upper and lower bounds on the 2-rank of the incidence matrices are derived. A lower bound on the minimum distance of the dual codes is proved, and it is shown that the bound is achieved if and only if the related maximal arc contains a hyperoval of the plane. The  binary linear codes of length 52 spanned by the incidence matrices of 2-$(52,4,1)$ designs associated with previously known and some newly found maximal arcs of degree 4 in projective planes of order 16 are analyzed and classified up to equivalence. The classification shows that some designs associated with maximal arcs in nonisomorphic planes generate equivalent codes. This phenomenon establishes new links between several of the known planes. A conjecture concerning the codes of maximal arcs in $PG(2,2^m)$ is formulated.

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

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.  

scholarly journals Bisimulations on Data Graphs

2018 ◽  
Vol 61 ◽  
pp. 171-213 ◽  
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.

scholarly journals Some properties of a dissimilarity measure for labeled graphs

2016 ◽  
pp. 85-94
Author(s):  
Nicolas Wicker ◽  
Canh Hao Nguyen ◽  
Hiroshi Mamitsuka
Keyword(s):  
Dissimilarity Measure ◽  
Labeled Graphs
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