Foster,s Theorems
المؤلف:
Foster, R. M
المصدر:
The Average Impedance of an Electrical Network." In Contributions to Applied Mechanics (Reissner Anniversary Volume). Ann Arbor, MI: Edwards Brothers
الجزء والصفحة:
...
17-3-2022
2707
Foster's Theorems
Let 
be the resistance distance matrix of a connected graph 
on 
nodes. Then Foster's theorems state that
where 
is the edge set of 
, and
where the latter sum runs over all pairs of adjacent edges 
and 
is the vertex degree of the vertex 
common to those edges (Palacios 2001).
REFERENCES
Foster, R. M. "The Average Impedance of an Electrical Network." In Contributions to Applied Mechanics (Reissner Anniversary Volume). Ann Arbor, MI: Edwards Brothers, pp. 333-340, 1949.
Foster, R. M. "An Extension of a Network Theorem Contributions to Applied Mechanics." IRE Trans. Cir. Th. 8, 75-76, 1961.
Klein, D. J. and Randić, M. "Resistance Distance." J. Math. Chem 12, 81-95, 1993.
Palacios, J. L. "Closed-Form Formulas for Kirchhoff Index." Int. J. Quant. Chem. 81, 135-140, 2001.
Tetali, P. "Random Walks and the Effective Resistance of Networks." J. Theor. Prob. 4, 101-109, 1991.
Tetali, P. "An Extension of Foster's Network Theorem." Combin. Prob. Comp. 3, 421-427, 1994.
Weinberg, L. "Kirchhoff's 'Third and Fourth Laws." IRE Trans. Cir. Th. 5, 8-30, 1958.
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