Cataloguing general graphs by point and line spectra Academic Article

abstract

• Certain perturbative expansions in physics are sums over all multigraphs with loops - i.e., graph-like structures in which each point can be connected to any other point, including itself, by an arbitrary number of lines. We treat the problem of exhibiting, or at least counting, all such objects for all reasonably small numbers of points and lines, as well as the associated problem of determining the number of labeled graphs corresponding to a given unlabeled one. Symbolic computation (specifically, Mathematica) has proven very useful here. It is helpful to classify the graphs further according to the distribution of the lines among the pairs of points (line spectrum) and simultaneously the distribution of the ends of the lines among the points (point spectrum). The basic tool is a generating function in which each coefficient is the number of general graphs with a given line spectrum and point spectrum. 1998 Elsevier Science B.V.

authors

• Borosh, Itshak
• Fulling, Stephen

published proceedings

• COMPUTER PHYSICS COMMUNICATIONS

author list (cited authors)

• Fulling, S. A., Borosh, I., & da Conturbia, A.

citation count

• 3

complete list of authors

• Fulling, SA||Borosh, I||da Conturbia, A

publication date

• December 1998

publisher

• Elsevier  Publisher

published in

• Computer Physics Communications  Journal

keywords

• Asymptotics
• Graph Theory
• Semiclassical Approximation
• Symbolic Computation

Digital Object Identifier (DOI)

• 10.1016/S0010-4655(98)00115-5

start page

• 93

end page

• 112

volume

• 115

issue

• 2-3

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fs0010-4655%2898%2900115-5