On signed graphs with just two distinct adjacency eigenvalues

Some regular signed graphs with only two distinct eigenvalues

“…In [9] the authors have provided a family containing infinitely many signed 4-regular graphs having just two distinct eigenvalues 2, −2. More precisely for each m ≥ 3, they construct a signed 4-regular graph with spectrum [2 m , −2 m ].…”

Signed graphs with two eigenvalues and vertex degree five

“…They are known to be regular, moreover every connected signed graph with 2 eigenvalues is strongly regular in the sense of [11]. All signed graphs with 2 eigenvalues and (vertex) degree at most 4 are explicitly determined in [8,12], and they can also be deduced from the results reported in [9]. In particular, there is an infinite family of those with degree 4.…”

“…Signed graphs with 2 eigenvalues have been investigated in [6,8,9,12] and some related references. They are known to be regular, moreover every connected signed graph with 2 eigenvalues is strongly regular in the sense of [11].…”

“…Those whose least eigenvalue is greater than −2 and those which are signed line graphs are also known and can be found in the same reference. There are also some sporadic results related to other classes of signed graphs with 2 eigenvalues [8,11,12]. Lastly, the Seidel matrix of a simple graph G can be seen as the adjacency matrix of the complete signed graph whose negative edges correspond to the edges of G. Accordingly, many results of [2,3] concerning graphs with exactly 2 eigenvalues of the Seidel matrix can be interpreted in the context of signed graphs.…”

Laplacian integral subcubic signed graphs

“…Therefore, there is a natural question: Which signed graphs have integral spectra? Recently, Hou et al [9] and Stanić [16] found out all integral signed graphs with vertex degree at most 4 and exactly 2 eigenvalues. Wang and Hou [14] gave all connected integral subcubic signed graphs.…”