Webtransitive graphs that are s-arc transitive but not (s+1)-arc transitive. More-over, there exist geodesic transitive graphs that are s-arc transitive but not (s+1)-arc transitive with arbitrarily large diameter if and only if s ∈ {1,2,3}. Theorem 1.1 is proved in Section 3 by analysing some well-known families ofdistance transitive graphs ... Web16 de dez. de 2010 · A further outcome of our analysis is a precise identification of which of these graphs are Cayley. We also investigate higher level of transitivity of the smallest known vertex-transitive graphs of a given degree and girth 6 and relate their constructions to near-difference sets. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:265-284, 2011

The girth of cubic graphs Royal Holloway Repository

WebA new approach to catalog small graphs of high even girth Vivek S. Nittoor [email protected] Independent Consultant & Researcher (formerly with the University of Tokyo) Abstract A catalog of a class of (3;g) graphs for even girth gis introduced in this pa-per. A (k;g) graph is a regular graph with degree kand girth g. This catalog of Web16 de dez. de 2010 · A further outcome of our analysis is a precise identification of which of these graphs are Cayley. We also investigate higher level of transitivity of the smallest … how to say yes in greek language

A new 5‐arc‐transitive cubic graph - ResearchGate

Webacts 2-arc-transitively on the quotient graph X. By Proposition 1.1, the class of finite connected 2-arc-transitive graphs can be divided into two subclasses as follows: (1) The 2-arc-transitive graphs Xwith the property that either (i) every nontrivial normal subgroup of Aut Xacts transitively on V(X),or (ii) every nontrivial normal subgroup WebARC–TRANSITIVE NON–CAYLEY GRAPHS FROM REGULAR MAPS P. GVOZDJAK and J. ˇSIR A´Nˇ Abstract. We prove that the underlying graphs of p-gonal r-valent orientably regular maps are arc-transitive but non-Cayley if r≥3 and pis a prime greater than r(r−1). 1. Introduction Orientable maps, i.e., embeddings of graphs in orientable surfaces ... Webconstructed half-arc-transitive graphs of valency 2k for all integers k > 2 (see also [12]). Note that a graph of valency 2 is a disjoint union of cycles and hence not half-arc-transitive. Thus the valency of a half-arc-transitive graph is at least 4. Over the last half a century, numerous papers have been published on half-arc- north london and south herts ramblers