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 re...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.展开更多
文摘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.
