Susana-Clara López

Edge-decompositions ofKn,ninto isomorphic copies of a given tree: DECOMPOSINGKn,nINTO TREES

We study the Häggkvist conjecture which states that, for each tree T with n edges, there is an edge-partition of the complete bipartite graph Kn;n into n isomorphic copies of T . We use the concept of bigraceful labelings, introduced in [7], which give rise to cyclic decompositions of Kn;n. When a tree T of size n is not known to be bigraceful it is shown, using similar techniques to the ones by Kézdy and Snevily [5], that T decomposes K2hn;2hn for some h dr=4e, where r is the radius of T . Moreover, if the base tree of T is bigraceful or if there is a vertex v in T such that jViðvÞj

Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

A d-regular graph is said to be superconnected if any disconnecting subset with cardinality at most d is formed by the neighbors of some vertex. A superconnected graph that remains connected after the failure of a vertex and its neighbors will be called vosperian. Let Γ be a vertex-transitive graph of degree d with order at least d+4. We give necessary and sufficient conditions for the vosperianity of Γ. Moreover, assuming that distinct vertices have distinct neighbors, we show that Γ is vosperian if and only if it is superconnected. Let G be a group and let S⊂G\{1} with S=S−1. We show that the Cayley graph, Cay(G, S), defined on G by S is vosperian if and only if G\(S∪{1}) is not a progression and for every non-trivial subgroup H and every a∈G, If moreover S is aperiodic, then Cay(G, S) is vosperian if and only if it is superconnected.

Langford sequences and a product of digraphs

Skolem and Langford sequences and their many generalizations have applications in numerous areas. The ? h -product is a generalization of the direct product of digraphs. In this paper we use the ? h -product and super edge-magic digraphs to construct an exponential number of Langford sequences with certain order and defect. We also apply this procedure to extended Skolem sequences.

Perfect (super) Edge-Magic Crowns

A graph G is called edge-magic if there is a bijective function f from the set of vertices and edges to the set

On the beta-number of forests with isomorphic components

\{1,2,\ldots ,|V(G)|+|E(G)|\}

Super Edge-Magic Models

{1,2,…,|V(G)|+|E(G)|} such that the sum

On total H-irregularity strength of the disjoint union of graphs

f(x)+f(xy)+f(y)