Degree distance and Gutman index of increasing trees
The Gutman index and degree distance of a connected graph G G are defined as Gut(G)=∑ {u,v}⊆V(G) d(u)d(v)d G (u,v), Gut(G)=∑{u,v}⊆V(G)d(u)d(v)dG(u,v), and DD(G)=∑ {u,v}⊆V(G) (d(u)+d(v))d G (u,v), DD(G)=∑{u,v}⊆V(G)(d(u)+d(v))dG(u,v), respectively, where d(u) d(...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Isfahan
2016-06-01
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| Series: | Transactions on Combinatorics |
| Subjects: | |
| Online Access: | http://www.combinatorics.ir/article_9915_00377372a764b119bb3640a24a194a64.pdf |
| Summary: | The Gutman index and degree distance of a connected graph G G are defined as
Gut(G)=∑ {u,v}⊆V(G) d(u)d(v)d G (u,v), Gut(G)=∑{u,v}⊆V(G)d(u)d(v)dG(u,v),
and
DD(G)=∑ {u,v}⊆V(G) (d(u)+d(v))d G (u,v), DD(G)=∑{u,v}⊆V(G)(d(u)+d(v))dG(u,v),
respectively, where d(u) d(u) is the degree of vertex u u and d G (u,v) dG(u,v) is the distance between vertices u u and v v. In this paper, through a recurrence equation for the Wiener index, we study the first two
moments of the Gutman index and degree distance of increasing trees. |
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| ISSN: | 2251-8657 2251-8665 |