Balancedness and spectra of signed graphs obtained by $$\dot{H}$$-join operation

Abstract

In this paper, we consider a generalized join operation, the $$\dot{H}$$ -join on signed graphs, where $$\dot{H}$$ is an arbitrary signed graph. We characterize the balancedness of the $$\dot{H}$$ -join graph, determine the adjacency spectra of graphs obtained by this operation on net regular graphs and the Laplacian spectra of graphs obtained on negatively regular graphs. Some additional consequences relevant to integral or cospectral graphs are also given.