The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or |Gv|≤2^4*3^6 or 2|G_v|\log_2(|G_v|/2)\leq |\V\Gamma| and that this last bound is tight. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.
COBISS.SI-ID: 1537132228
In this paper graphs admitting a half-arc-transitive group action with at most five alternets are considered. In particular, it is shown that if the number of alternets is at most three, then the graph is necessarily tightly attached, but there exist graphs with four and graphs with five alternets which are not tightly attached.
COBISS.SI-ID: 1536241092
Let G denote a finite abelian group with identity 1 and let S denote an inverse-closed subset of G\{1}, which generates G and for which there exists s in S, such that (S\{s,s^{-1}}) is a proper subgroup of G. In this paper we obtain the complete classification of distance-regular Cayley graphs Cay(G;S) for such pairs of G and S.
COBISS.SI-ID: 1536382660
This discussion is published in the esteemed general scientific mathematical journal Proc. Lond. Math. Soc. that ranks in A' (ARRS methodology). It solves the hamiltonicity problem for cubic Cayley graphs on groups with respect to genereting sets consisting of an involution, a non-involution of odd order and the inverse of this non-involution.
COBISS.SI-ID: 1024390740
Dragan Stevanovića published a scientific monograph Spectral Radius of Graphs (published Elsevier) dedicated to developments, proofs, and open problems for spectral graph theory.
COBISS.SI-ID: 1536992708