On the number of components of (k,g)-cages after vertex deletion

Authors:
Yuqing Lin;Camino Balbuena;Mirka Miller
Affiliations:
School of Electrical Engineering and Computer Science, The University of Newcastle, NSW 2308, Australia;Department de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Spain;School of Electrical Engineering and Computer Science, The University of Newcastle, NSW 2308, Australia and Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

A (k,g)-cage is a k-regular graph of girth g and with the least possible number of vertices. In this paper, we investigate the problem of how many connected components there will be after removing a cutset of up to k vertices from a (k,g)-cage.