For any prime power q ≥ 3, we consider two infinite series of bipartite q–regular edge–transitive graphs of orders 2q and 2q which are induced subgraphs of regular generalized 4–gon and 6–gon, respectively. We compare these two series with two families of graphs,H3(p) andH5(p), p is a prime, constructed recently by Wenger ([26]), which are new examples of extremal graphs without 6– and 10–cycle...

MOTIVATION Molecular diagnostics aims at classifying diseases into clinically relevant sub-entities based on molecular characteristics. Typically, the entities are split into subgroups, which might contain several variants yielding a hierarchical model of the disease. Recent years have introduced a plethora of new molecular screening technologies to molecular diagnostics. As a result molecular ...

A graph is half-arc-transitive if its automorphism group acts transitively on its vertex set, edge set, but not arc set. Let p and q be primes. It is known that no tetravalent half-arc-transitive graphs of order 2p2 exist and a tetravalent half-arctransitive graph of order 4p must be non-Cayley; such a non-Cayley graph exists if and only if p − 1 is divisible by 8 and it is unique for a given o...