Abstract

This work deals with complementarity spectra of connected graphs and, specifically, with the associated concept of spectral capacity of a finite set of connected graphs. The cardinality of the complementarity spectrum of a connected graph G serves as lower bound for the number of connected induced subgraphs of G. Motivated by this observation, we establish various results on cardinality of complementarity spectra. Special attention is paid to the asymptotic behavior of spectral capacities as the number of vertices goes to infinity.