RESISTANCE DISTANCE IN WHEELS AND FANS

被引：70

作者：

Bapat, R. B. ^{[1
]}

Gupta, Somit ^{[2
]}

机构：

[1] Indian Stat Inst, New Delhi 110016, India

[2] Natl Inst Technol Karnataka, Mangalore 575025, India

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2010年 / 41卷 / 01期

关键词：

Wheel graph; fan graph; resistance distance; generalized Fibonacci numbers; squaring a rectangle;

D O I：

10.1007/s13226-010-0004-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The wheel graph is the join of a single vertex and a cycle, while the fan graph is the join of a single vertex and a path. The resistance distance between any two vertices of a wheel and a fan is obtained. The resistances are related to Fibonacci numbers and generalized Fibonacci numbers. The derivation is based on evaluating determinants of submatrices of the Laplacian matrix. A combinatorial argument is also illustrated. A connection with the problem of squaring a rectangle is described.

引用

页码：1 / 13

页数：13

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