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Graph-functions associated with an edge-property
Citation
Dong, F. M., Hendy, M. D., Teo, K. L., & Little, C. H. C. (2004). Graph-functions associated with an edge-property. Australasian Journal of Combinatorics, 30, 3-20. http://ajc.maths.uq.edu.au/pdf/30/ajc_v30_p003.pdf
Abstract
Let P be an edge-property of graphs. For any graph G we construct a polynomial Ψ(G, η,P), in an indeterminate η, in which the coefficient of ηr for any r ≥ 0 gives the number of subsets of E(G) that have
cardinality r and satisfy P. An example is the well known matching polynomial of a graph. After studying the properties of Ψ(G, η,P) in general, we specialise to two particular edge-properties: that of being an
edge-covering and that of inducing an acyclic subgraph. The resulting polynomials, called the edge-cover and acyclic polynomials respectively, are studied and recursive formulae for computing them are derived. As
examples we calculate these polynomials for paths and cycles.
Date Issued
2004
Publisher
Combinatorial Mathematics Society of Australasia
Journal
Australasian Journal of Combinatorics