An edge cut of a connected graph is 4-restricted if it disconnects this graph with each component having order at least four. The size of minimum 4-restricted edge cuts of graph G is called its 4-restricted edge connectivity and is denoted by 4(G). Let 4(G)=min{ (F ) : F is a connected vertex-induced subgraph of order four of graph G}, where (F ) denotes the number of edges of graph G with exac...

We explore properties of edge colorings of graphs defined by set intersections. An edge coloring of a graphG with vertex set V ={1,2, . . . ,n} is called transitive if one can associate sets F1,F2, . . . ,Fn to vertices of G so that for any two edges ij,kl∈E(G), the color of ij and kl is the same if and only if Fi∩Fj =Fk∩Fl. The term transitive refers to a natural partial order on the color set...

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...