TITLE:
Reciprocal Complementary Wiener Numbers of Non-Caterpillars
AUTHORS:
Yanli Zhu, Fuyi Wei, Feng Li
KEYWORDS:
Reciprocal Complementary Wiener Number, Wiener Number, Caterpillar
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.3,
February
26,
2016
ABSTRACT: The reciprocal complementary Wiener number of a connected graph G is defined as where is the vertex set. is the distance between vertices u and v, and d is the diameter of G. A tree is known as a caterpillar if the removal of all pendant vertices makes it as a path. Otherwise, it is called a non-caterpillar. Among all n-vertex non-cater- pillars with given diameter d, we obtain the unique tree with minimum reciprocal complementary Wiener number, where . We also determine the n-vertex non-caterpillars with the smallest, the second smallest and the third smallest reciprocal complementary Wiener numbers.