A graph is said to be $(\Delta,\delta)$-bidegreed if vertices all have one of two possible degrees: the maximum degree $\Delta$ or the minimum degree $\delta$, with $\Delta\neq \delta$. We show that in the set of connected $(\Delta,1)$-bidegreed graphs, other than trees, with prescribed degree sequence, the graphs minimizing the adjacency matrix spectral radius cannot have vertices adjacent to $\Delta-1$ vertices of degree $1$, that is, there are not any hanging trees. Further we consider the limit point for the spectral radius of $(\Delta,1)$-bidegreed graphs when degree $\Delta$ vertices are inserted in each edge between any two degree $\Delta$ vertices
On the structure of bidegreed graphs with minimal spectral radius
BELARDO, FRANCESCO
2014-01-01
Abstract
A graph is said to be $(\Delta,\delta)$-bidegreed if vertices all have one of two possible degrees: the maximum degree $\Delta$ or the minimum degree $\delta$, with $\Delta\neq \delta$. We show that in the set of connected $(\Delta,1)$-bidegreed graphs, other than trees, with prescribed degree sequence, the graphs minimizing the adjacency matrix spectral radius cannot have vertices adjacent to $\Delta-1$ vertices of degree $1$, that is, there are not any hanging trees. Further we consider the limit point for the spectral radius of $(\Delta,1)$-bidegreed graphs when degree $\Delta$ vertices are inserted in each edge between any two degree $\Delta$ verticesPubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.