21,467 research outputs found
Reconstruction of graded groupoids from graded Steinberg algebras
We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal
neutrally-graded component from the ring structure of its graded Steinberg algebra over
any commutative integral domain with 1, together with the embedding of the canonical
abelian subring of functions supported on the unit space. We deduce that
diagonal-preserving ring isomorphism of Leavitt path algebras implies -isomorphism
of -algebras for graphs and in which every cycle has an exit.
This is a joint work with Joan Bosa, Roozbeh Hazrat and Aidan Sims.Universidad de Málaga. Campus de Excelencia internacional Andalucía Tec
Path graphs
The concept of a line graph is generalized to that of a path graph. The path graph Pk(G) of a graph G is obtained by representing the paths Pk in G by vertices and joining two vertices whenever the corresponding paths Pk in G form a path Pk+1 or a cycle Ck. P3-graphs are characterized and investigated on isomorphism and traversability. Trees and unicyclic graphs with hamiltonian P3-graphs are characterized
Isomorphisms and traversability of directed path graphs
The concept of a line digraph is generalized to that of a directed path graph. The directed path graph \forw P_k(D) of a digraph is obtained by representing the directed paths on vertices of by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in form a directed path on vertices or form a directed cycle on vertices in . In this introductory paper several properties of \forw P_3(D) are studied, in particular with respect to isomorphism and traversability. In our main results, we characterize all digraphs with \forw P_3(D)\cong D, we show that \forw P_3(D_1)\cong\forw P_3(D_2) ``almost always'' implies , and we characterize all digraphs with Eulerian or Hamiltonian \forw P_3-graphs
On the Lengths of Symmetry Breaking-Preserving Games on Graphs
Given a graph , we consider a game where two players, and ,
alternatingly color edges of in red and in blue respectively. Let be
the maximum number of moves in which is able to keep the red and the blue
subgraphs isomorphic, if plays optimally to destroy the isomorphism. This
value is a lower bound for the duration of any avoidance game on under the
assumption that plays optimally. We prove that if is a path or a cycle
of odd length , then . The lower
bound is based on relations with Ehrenfeucht games from model theory. We also
consider complete graphs and prove that .Comment: 20 page
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