Let G be a connected k-regular bipartite graph with bipartition $V(G) = X \cap Y$ and adjacency matrix A. We say G is det-extremal if per(A) = |det(A)|. Det-extremal k-regular bipartite graphs exist only for k = 2 or 3. McCuaig has characterized the det-extremal 3-connected cubic bipartite graphs. We extend McCuaig's result by determining the structure of det-extremal cubic bipartite graphs of connectivity two. We use our results to determine which numbers can occur as orders of det-extremal connected cubic bipartite graphs, thus solving a problem due to H. Gropp.

Det-Extremal Cubic Bipartite Graphs

FUNK, Martin;LABBATE, Domenico;
2003-01-01

Abstract

Let G be a connected k-regular bipartite graph with bipartition $V(G) = X \cap Y$ and adjacency matrix A. We say G is det-extremal if per(A) = |det(A)|. Det-extremal k-regular bipartite graphs exist only for k = 2 or 3. McCuaig has characterized the det-extremal 3-connected cubic bipartite graphs. We extend McCuaig's result by determining the structure of det-extremal cubic bipartite graphs of connectivity two. We use our results to determine which numbers can occur as orders of det-extremal connected cubic bipartite graphs, thus solving a problem due to H. Gropp.
2003
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11563/416
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 5
social impact