### Abstract

This report considers the resistance distance as a recently proposed new intrinsic metric on (molecular) graphs, and in particular, the sum R over resistance distances between all pairs of vertices is considered as a graph invariant. It has been proved that R(G_{N}) > R(K_{N}), where G_{N} denotes a connected graph containing N vertices and K_{N} denotes a complete graph containing N vertices. The formulas to obtain the R for two classes of regular graphs (cycles and complete graphs) are derived. Numerical values of R for four Platonic molecules are also given. They ordered the considered Platonic solids as the icosahedron, the cube, the octahedron, and the tetrahedron according to complexity of their Schlegel graphs. This order agrees with those obtained by many other, frequently used descriptors.

Original language | English |
---|---|

Pages (from-to) | 217-225 |

Number of pages | 9 |

Journal | International Journal of Quantum Chemistry |

Volume | 71 |

Issue number | 3 |

Publication status | Published - 1999 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*International Journal of Quantum Chemistry*,

*71*(3), 217-225.

**Resistance distance in regular graphs.** / Lukovits, I.; Nikolić, S.; Trinajstić, N.

Research output: Contribution to journal › Article

*International Journal of Quantum Chemistry*, vol. 71, no. 3, pp. 217-225.

}

TY - JOUR

T1 - Resistance distance in regular graphs

AU - Lukovits, I.

AU - Nikolić, S.

AU - Trinajstić, N.

PY - 1999

Y1 - 1999

N2 - This report considers the resistance distance as a recently proposed new intrinsic metric on (molecular) graphs, and in particular, the sum R over resistance distances between all pairs of vertices is considered as a graph invariant. It has been proved that R(GN) > R(KN), where GN denotes a connected graph containing N vertices and KN denotes a complete graph containing N vertices. The formulas to obtain the R for two classes of regular graphs (cycles and complete graphs) are derived. Numerical values of R for four Platonic molecules are also given. They ordered the considered Platonic solids as the icosahedron, the cube, the octahedron, and the tetrahedron according to complexity of their Schlegel graphs. This order agrees with those obtained by many other, frequently used descriptors.

AB - This report considers the resistance distance as a recently proposed new intrinsic metric on (molecular) graphs, and in particular, the sum R over resistance distances between all pairs of vertices is considered as a graph invariant. It has been proved that R(GN) > R(KN), where GN denotes a connected graph containing N vertices and KN denotes a complete graph containing N vertices. The formulas to obtain the R for two classes of regular graphs (cycles and complete graphs) are derived. Numerical values of R for four Platonic molecules are also given. They ordered the considered Platonic solids as the icosahedron, the cube, the octahedron, and the tetrahedron according to complexity of their Schlegel graphs. This order agrees with those obtained by many other, frequently used descriptors.

UR - http://www.scopus.com/inward/record.url?scp=0001658791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001658791&partnerID=8YFLogxK

M3 - Article

VL - 71

SP - 217

EP - 225

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 3

ER -