Article,

Another look at the degree-Kirchhoff index

, and .
International Journal of Quantum Chemistry, 111 (14): 3453--3455 (2011)
DOI: 10.1002/qua.22725

Abstract

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 $$R' (G) 2Ełeft( N - 2 + 1 D + 1 \right).$$ 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

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