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Functions on adjacent vertex degrees of trees with given degree sequence

Hua Wang — 2014

Open Mathematics

In this note we consider a discrete symmetric function f(x, y) where f ( x , a ) + f ( y , b ) f ( y , a ) + f ( x , b ) f o r a n y x y a n d a b , associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as u v E ( T ) f ( d e g ( u ) , d e g ( v ) ) , are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randic index follow as corollaries. The extremal structures...

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