Abstract
Let [Formula: see text] be a simple graph with an adjacency matrix [Formula: see text]. Then the eigenvalues of [Formula: see text] are the eigenvalues of [Formula: see text] and form the spectrum, [Formula: see text] of [Formula: see text]. The graph [Formula: see text] is integral if [Formula: see text] consists of only integers. In this paper, we define three new operations on graphs and characterize all integral graphs in the resulting families. The resulting families are denoted by [Formula: see text], and [Formula: see text]. These characterizations allow us to exhibit many new infinite families of integral graphs.
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