The change in index of a graph resulting from the attachment of a pendant edge

Citation

Bell FK & Rowlinson P (1988) The change in index of a graph resulting from the attachment of a pendant edge. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 108 (1-2), pp. 67-74. https://doi.org/10.1017/S0308210500026524

Abstract
Conditions are obtained under which a graph G', obtained from a graph G by the attachment of a pendant edge, may be regarded as a perturbation of G. In this situation the index of G' is expressed as the sum of a convergent series whose terms are determined by the spectrum and certain angles of G.

Journal
Proceedings of the Royal Society of Edinburgh: Section A Mathematics: Volume 108, Issue 1-2