On a problem of ore on maximal trees
Snehal B. Rao · Journal of the Australian Mathematical Society · 1970
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.