A graph is pseudo 2–factor isomorphic if the numbers of circuits of length congruent to zero modulo four in each of its 2–factors, have the same parity. We prove that there exist no pseudo 2–factor isomorphic 1 2 Pseudo 2–Factor Isomorphic k–regular bipartite graphs for k ≥ 4. We also propose a characterization for 3-connected pseudo 2–factor isomorphic… (More)
In this paper we obtain (q + 3)–regular graphs of girth 5 with fewer vertices than previously known ones for q = 13, 17, 19 and for any prime q ≥ 23 performing operations of reductions and amalgams on the Levi graph Bq of an elliptic semiplane of type C. We also obtain a 13–regular graph of girth 5 on 236 vertices from B11 using the same technique.
A bipartite graph is pseudo 2–factor isomorphic if all its 2–factors have the same parity of number of circuits. In a previous paper we have proved that pseudo 2–factor isomorphic k–regular bipartite graphs exist only for k ≤ 3, and partially characterized them. In particular we proved that the only essentially 4–edge-connected pseudo 2–factor isomor-phic… (More)
We show that a digraph which contains a directed 2-factor and has minimum in-degree and out-degree at least four has two non-isomorphic directed 2-factors. As a corollary we deduce that every graph which contains a 2-factor and has minimum degree at least eight has two non-isomorphic 2-factors. In addition we construct: an infinite family of strongly… (More)
In this note we construct a new infinite family of (q − 1)-regular graphs of girth 8 and order 2q(q − 1) 2 for all prime powers q 16, which are the smallest known so far whenever q − 1 is not a prime power or a prime power plus one itself.