Book ChapterDOI
Axiomatic Characterization of the Interval Function of a Bipartite Graph
Manoj Changat,Ferdoos Hossein Nezhad,N. Narayanan +2 more
- pp 96-106
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TLDR
A new axiom is introduced: for any x,y,z, R(x,y) = x, y = Rightarrow y in R (x,z) or x in R(y,Z) for any \( x,Y,z \in V\),Abstract:
The axiomatic approach with the interval function and induced path transit function of a connected graph is an interesting topic in metric and related graph theory. In this paper, we introduce a new axiom:
(bp) for any \( x,y,z \in V\), \(R(x,y)=\{x,y\} \Rightarrow y\in R(x,z)\) or \(x\in R(y,z)\).read more
Citations
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Journal ArticleDOI
Betweenness in graphs: A short survey on shortest and induced path betweenness
TL;DR: The results are surveyed as answers to these questions available from the research papers on the interval function of special graphs using some set of first order axioms defined on an arbitrary transit function.
Journal ArticleDOI
Interval function, induced path function, (claw, paw)-free graphs and axiomatic characterizations
TL;DR: This paper presents characterizations of (claw, paw)-free graphs using axiom (cp) on the standard path transit functions on graphs, namely the interval function, the induced path function, and the all-paths function.
Posted Content
The Interval function, Ptolemaic, distance hereditary, bridged graphs and axiomatic characterizations.
TL;DR: The class of graphs that are characterized include the important class of Ptolemaic graphs and some proper superclasses of P toleMAic graphs: the distance hereditary graphs and the bridged graphs.
References
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Journal ArticleDOI
Finite Sholander trees, trees, and their betweenness
TL;DR: Finite Sholander trees are trees in the usual sense and a new axiomatic characterization of the interval function of a tree is yielded.
Journal ArticleDOI
A Note on the Interval Function of a Disconnected Graph
TL;DR: The Mulder-Nebeský characterization of the interval function of a connected graph to the disconnected case is extended and one axiom needs to be adapted, but also a new axiom is needed in addition.
Journal ArticleDOI
The Induced Path Transit Function and the Pasch Axiom
TL;DR: In this article, the authors characterize all graphs for which the induced path transit function satisfies the Pasch axiom, which is a strong geometric property which was noted and discussed even from the period of Euclid.
Book ChapterDOI
Axiomatic Characterization of Claw and Paw-Free Graphs Using Graph Transit Functions
TL;DR: This paper introduces the first order axiom cp, which is satisfied on the interval function, induced path transit function and all-paths transit function of a connected simple and finite graph and presents characterizations of claw and paw-free graphs using this axiom.
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