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.
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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
The All-Paths Transit Function of a Graph
TL;DR: A transit function R on a set V is characterized by transit axioms as mentioned in this paper, where R(u, u, u) is a transit function satisfying the axiomatization of U(U, U) for all paths in a connected graph.
Journal ArticleDOI
The induced path convexity, betweenness, and svelte graphs
TL;DR: The induced path interval J(u,v) consists of the vertices on the induced paths between u and v in a connected graph G, in which the induced path intervals define a proper betweenness.
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Transit functions on graphs (and posets)
TL;DR: The notion of transit functions is introduced in this paper to present a unifying approach for results and ideas on intervals, convexities and betweenness in graphs and configurations, and the main idea of transit function is that of transferring problems and ideas of one transit function to the other.
Journal ArticleDOI
Induced path transit function, monotone and Peano axioms
Manoj Changat,Joseph Mathew +1 more
TL;DR: The induced path transit function J (u; v) in a graph consists of the set of all vertices lying on any induced path between the vertices u and v, and is said to satisfy the Peano axiom.
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