The dumbbell graph, denoted by D-a,D-b,D-c is a bicyclic graph consisting of two vertex-disjoint cycles C-a and C-b joined by a path Pc+3 (C >= -1)having only its end-vertices in common with the two cycles. By using a new cospectral invariant for (r, r + 1)-almost regular graphs, we will show that almost all dumbbell graphs (without cycle C-4 as a subgraph) are determined by the adjacency spectrum. © 2009 Elsevier Inc. All rights reserved.
A note on the spectral characterization of dumbbell graphs
BELARDO, FRANCESCO;LI MARZI, Enzo
2009-01-01
Abstract
The dumbbell graph, denoted by D-a,D-b,D-c is a bicyclic graph consisting of two vertex-disjoint cycles C-a and C-b joined by a path Pc+3 (C >= -1)having only its end-vertices in common with the two cycles. By using a new cospectral invariant for (r, r + 1)-almost regular graphs, we will show that almost all dumbbell graphs (without cycle C-4 as a subgraph) are determined by the adjacency spectrum. © 2009 Elsevier Inc. All rights reserved.File in questo prodotto:
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