Linda EROH1, Ralucca GERA2, Steven J. WINTERS1
1. Department of Mathematics, University of Wisconsin Oshkosh, Oshkosh, WI $54901$, USA; 2. Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA $93943$, USA
Abstract:A delivery person must leave the central location of the business, deliver packages at a number of addresses, and then return. Naturally, he/she wishes to reduce costs by finding the most efficient route. This motivates the following:
Given a set of k distinct vertices S={x1, x2, …, xk} in a simple graph G, the closed k-stop-distance of set S is defined to be
where P(S) is the set of all permutations of S. That is the same as saying that dk(S) is the length of a shortest closed walk through the vertices {x1, …, xk}.
The closed 2-stop distance is twice the standard distance between two vertices.We study the closed k-stop center and closed k-stop periphery of a graph, for k=3.
Key words:Central appendage number; peripheral appendage number; Steiner distance
Source:Acta Mathematica Sinica, English Series.2012, 28(3) | 
