On the Spectral-Equipartite Graphs and Eccentricity-Equipartite Graphs

Abstract

Let G = (V, E) be a graph of order 2n. If A ⊆ V and hAi ∼= hV \Ai, then A is said to be isospectral. If for every n-element subset A of V we have hAi ∼= hV \Ai, then we say that G is spectral-equipartite. In [1], Igor Shparlinski communicated with Bibak et al., proposing a full characterization of spectral-equipartite graphs. In this paper, we gave a characterization of disconnected spectral-equipartite graphs. Moreover, we introduced the concept eccentricity-equipartite graphs.