Triangles in labelled cubic graphs

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Abstract

No cubic graph has an odd number of points. A method is found of calculating the number tp of labelled connected cubic graphs with 2p points rooted at triangle. The method presupposes knowledge of the numbers qk of labelled connected cubic graphs with 2k points and k < p. Labelled connected cubic graphs have already been counted by Read, so this allows determination of the mean number tp /qp of triangles in a labelled connected cubic graph with 2p points, for all p > 1. It is shown that tp /qp → 4/3 as p →∞.
Original languageEnglish
Title of host publicationCombinatorial Mathematics
Subtitle of host publicationProceedings of the International Conference on Combinatorial Theory Canberra, August 16-27, 1977
EditorsD A Holton, Jennifer Seberry
Place of PublicationBerlin Germany
PublisherSpringer
Pages337-345
Number of pages9
Volume686
DOIs
Publication statusPublished - 1978
Externally publishedYes

Publication series

NameLecture Notes in Mathematics
PublisherSpringer
Volume686

Cite this

Wormald, N. C. (1978). Triangles in labelled cubic graphs. In D. A. Holton, & J. Seberry (Eds.), Combinatorial Mathematics: Proceedings of the International Conference on Combinatorial Theory Canberra, August 16-27, 1977 (Vol. 686, pp. 337-345). (Lecture Notes in Mathematics; Vol. 686). Springer. https://doi.org/10.1007/BFb0062550