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On a problem of ore on maximal trees

Published online by Cambridge University Press:  09 April 2009

S. B. Rao
S. B. Rao
Affiliation:
Indian Statistical InstituteCalcutta 35, India
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We consider only graphs without loops or multiple edges. Pertinent definitions are given below. For notation and other definitions we generally follow Ore [1].

A connected graph G = (X, E) is said to have the property P if for every maximal tree T of G there exists a vertex aT of G such that distance between aT and x is same in T as in G for every x in X. The following problem has been posed by Ore (see [1] page 103, problem 4): Determine the graphs with property P. This paper presents a solution to the above problem in the finite case.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 3 , August 1970 , pp. 379 - 380
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Ore, O., Theory of graphs (American Mathematical Society Colloquium Publication, 38, Providence, Rhode Island, 1962).Google Scholar