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A Note on the Interval Function of a Disconnected Graph

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Changat M., Hossein Nezhad F., Mulder H. M., Narayanan N.
Discussiones Mathematicae Graph Theory
|
2017
|
tom 38
|
nr 1
39-48
EN
In this note we extend the Mulder-Nebeský characterization of the interval function of a connected graph to the disconnected case. One axiom needs to be adapted, but also a new axiom is needed in addition.
2
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n-ary transit functions in graphs

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Changat M., Mathews J., Peterin I., Narasimha-Shenoi P.
Discussiones Mathematicae Graph Theory
|
2010
|
tom 30
|
nr 4
671-685
EN
n-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural n-ary generalization of geodesicaly convexity. Furthermore, we generalize the betweenness axioms to n-ary transit functions and discuss the connectivity conditions for underlying hypergraph. Also n-ary all paths transit function is considered.
3
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The periphery graph of a median graph

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Brešar B., Changat M., Subhamathi A., Tepeh A.
Discussiones Mathematicae Graph Theory
|
2010
|
tom 30
|
nr 1
17-32
EN
The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are path-like median graphs with arbitrarily large geodetic number. Peripheral expansion with respect to periphery graph is also considered, and connections with the concept of crossing graph are established.
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