Another look at the degree-Kirchhoff index

Let G be an arbitrary graph with vertex set {1,2, …,N} and degrees di ≤ D, for fixed D and all i, then for the index R′(G) = ∑i < jdidjRij we show that $$R' (G) \ge 2\vert E\vert \left( {N - 2 + {1 \over {D + 1}}} \right).$$ We also show that the minimum of R′(G) over all N‐vertex graphs is...

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Bibliographic Details
Published in:International journal of quantum chemistry 2011-11, Vol.111 (14), p.3453-3455
Main Authors: Palacios, José Luis, Renom, José Miguel
Format: Article
Language:English
Subjects:
Kirchhoff index
star graph
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Summary:Let G be an arbitrary graph with vertex set {1,2, …,N} and degrees di ≤ D, for fixed D and all i, then for the index R′(G) = ∑i < jdidjRij we show that $$R' (G) \ge 2\vert E\vert \left( {N - 2 + {1 \over {D + 1}}} \right).$$ We also show that the minimum of R′(G) over all N‐vertex graphs is attained for the star graph and its value is 2N2 − 5N + 3. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011
ISSN:0020-7608
1097-461X
DOI:10.1002/qua.22725