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
Axiomatic characterization of the interval function of a graph
TL;DR: Nebesky et al. as mentioned in this paper characterized the interval function of finite connected graphs by axioms in terms of properties of the functions F:VxV->2^V-{[email protected]?}.
Journal ArticleDOI
The induced paths in a connected graph and a ternary relation determined by them
TL;DR: In this paper, it was shown that there is no sentence σ of the first-order logic such that a ternary structure (X0, T0) with a connected underlying graph G is the B-structure of G if and only if σ satisfies σ.
Journal ArticleDOI
A Characterization of the Interval Function of a (Finite or Infinite) Connected Graph
TL;DR: In this article, the authors give a characterization of the interval function of each connected graph, which is very important for studying properties of a finite connected graph which depend on the distance between vertices.
Journal ArticleDOI
The induced path function, monotonicity and betweenness
TL;DR: In this article, the authors considered the problem of axiomatic characterizations of the induced path function J of a connected graph G. This function is a special instance of a transit function.
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