Abstract
We apply a circuit chasing technique to distance-biregular graphs of girth divisible by four to derive a parameter restriction. As an application, we give a classification of distance-biregular graphs of girth divisible by four with trivalent vertices.
Similar content being viewed by others
References
Boshier, A., Nomura, K.: A remark on the intersection arrays of distance-regular grahs. J. Com. Theory, Ser. B44, 147–153 (1988)
Brouwer, A.E., Cohen, A.M. Neumaier, A.: Distance-regular graphs, Springer Verlag, Berlin, Heidelberg, 1989
Fuglister, F.: On generalized Moore geometries, I. Discrete Math.67, 249–258 (1987)
Fuglister, F.: On generalized Moore geometries, II. Discrete Math.67, 259–269 (1987)
Ito T.: Bipartite distance-regular graphs of valency 3. Linear Algebra Appl.46, 195–213 (1982)
Mohar, B., Shawe-Taylor, J.: Distance-biregular graphs with 2-valent vertices and distance-regular line graphs. J. Comb. Theory, Ser. B38, 193–203 (1985)
Nomura, K.: Intersection diagrams of distance-biregular graphs. J. Comb. Theory, Ser. B50, 214–221 (1990)
Wilbrink, H.A., Brouwer, A.E.: A (57, 14, 1) strongly regular graph does not exist. Indag. Math.45, 117–121 (1983)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zuzuki, H. On distance-biregular graphs of girth divisible by four. Graphs and Combinatorics 10, 61–65 (1994). https://doi.org/10.1007/BF01202471
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01202471