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Resistance distance in regular graphs

✍ Scribed by I. Lukovits; S. Nikolić; N. Trinajstić

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
240 KB
Volume
71
Category
Article
ISSN
0020-7608

No coin nor oath required. For personal study only.

✦ Synopsis

This report considers the resistance distance as a recently proposed new

Ž

. 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

vertices and K denotes a complete graph containing N vertices. The formulas to obtain N Ž . 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.

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