Another look at the degree-Kirchhoff index

José Luis Palacios; José Miguel Renom

doi:10.1002/qua.22725

Another look at the degree-Kirchhoff index

José Luis Palacios, José Miguel Renom

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

Let G be an arbitrary graph with vertex set {1,2, ...,N} and degrees d _i ≤ D, for fixed D and all i, then for the index R′(G) = Σ_i<jd_jd_jR_ij we show that R′(G) ≥ 2 |E| (N - 2 + 1/D + 1). 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.

Original language	English
Pages (from-to)	3453-3455
Number of pages	3
Journal	International Journal of Quantum Chemistry
Volume	111
Issue number	14
DOIs	https://doi.org/10.1002/qua.22725
State	Published - 15 Nov 2011
Externally published	Yes

Keywords

Kirchhoff index
star graph

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10.1002/qua.22725

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abstract = "Let G be an arbitrary graph with vertex set {1,2, ...,N} and degrees d i ≤ D, for fixed D and all i, then for the index R′(G) = ΣidjdjRij we show that R′(G) ≥ 2 |E| (N - 2 + 1/D + 1). 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.",

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AB - Let G be an arbitrary graph with vertex set {1,2, ...,N} and degrees d i ≤ D, for fixed D and all i, then for the index R′(G) = ΣidjdjRij we show that R′(G) ≥ 2 |E| (N - 2 + 1/D + 1). 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.

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ER -

Another look at the degree-Kirchhoff index

Abstract

Keywords

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