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.File in questo prodotto:
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