Edge-girth-regular graphs

Robert Jajcay (Author), György Kiss (Author), Štefko Miklavič (Author)

Abstract

We consider a new type of regularity we call edge-girth-regularity. An edge-girth-regular ▫$(v, k, g, \lambda)$▫-graph ▫$\varGamma$▫ is a ▫$k$▫-regular graph of order ▫$v$▫ and girth ▫$g$▫ in which every edge is contained in ▫$\lambda$▫ distinct ▫$g$▫-cycles. This concept is a generalization of the well-known concept of ▫$(v, k, \lambda)$▫-edge-regular graphs (that count the number of triangles) and appears in several related problems such as Moore graphs and cage and degree/diameter problems. All edge- and arc-transitive graphs are edge-girth-regular as well. We derive a number of basic properties of edge-girth-regular graphs, systematically consider cubic and tetravalent graphs from this class, and introduce several constructions that produce infinite families of edge-girth-regular graphs. We also exhibit several surprising connections to regular embeddings of graphs in orientable surfaces.

Keywords

girth;edge-regular graph;edge-girth-regular graph;regular embeddings of graphs in orientable surfaces;Moore graphs;

Data

Language:	English
Year of publishing:	2018
Typology:	1.01 - Original Scientific Article
Organization:	UP - University of Primorska
UDC:	519.17
COBISS:	1540315332
ISSN:	0195-6698
Views:	1972
Downloads:	370
Average score:	0 (0 votes)
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