Reciprocal Complementary Wiener Numbers of Non-Caterpillars
نویسندگان
چکیده
The reciprocal complementary Wiener number of a connected graph G is defined as ( ) { } ( ) ( ) | ∑ u v V G RCW G d d u v G ⊆ = + − , 1 1 , where ( ) V G is the vertex set. ( ) | d u v G , 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-caterpillars with given diameter d, we obtain the unique tree with minimum reciprocal complementary Wiener number, where d n ≤ ≤ − 4 3 . We also determine the n-vertex non-caterpillars with the smallest, the second smallest and the third smallest reciprocal complementary Wiener numbers.
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