The transmission of a vertex is defined as the sum of the lengths of all shortest paths between the chosen vertex and all other vertices in G. The transmission of a graph G is the sum of the transmissions of all its vertices which is nothing but twice its Wiener index. In location theory, sets of vertices, with the minimum (or maximum) distance in a graph, play a special role because they form target sets for locations of facilities. The framework is made more general by considering the sum of distances to a specified multiset of vertices referred to as profiles. In this paper, we have defined paired transmission of vertices for a network as a special case of profiles, referred to as a paired facility location.

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Paired Transmission in Networks

  • Jessy Sujana G,
  • Jane Olive Sharon,
  • J. Anitha

摘要

The transmission of a vertex is defined as the sum of the lengths of all shortest paths between the chosen vertex and all other vertices in G. The transmission of a graph G is the sum of the transmissions of all its vertices which is nothing but twice its Wiener index. In location theory, sets of vertices, with the minimum (or maximum) distance in a graph, play a special role because they form target sets for locations of facilities. The framework is made more general by considering the sum of distances to a specified multiset of vertices referred to as profiles. In this paper, we have defined paired transmission of vertices for a network as a special case of profiles, referred to as a paired facility location.