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Deletion and contraction identities for the resistance values and the Kirchhoff index
Author(s) -
Cinkir Zubeyir
Publication year - 2011
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.22942
Subject(s) - upper and lower bounds , contraction (grammar) , graph , mathematics , quantum , edge contraction , combinatorics , index (typography) , topological index , quantum graph , discrete mathematics , physics , quantum mechanics , mathematical analysis , computer science , line graph , voltage graph , medicine , world wide web
We establish identities, which we call deletion and contraction identities, for the resistance values on an electrical network. As an application of these identities, we give an upper bound to the Kirchhoff index of a molecular graph. Our upper bound, expressed in terms of the set of vertices and the edge connectivity of the graph, improves previously known upper bounds. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010