Infinite families of Q-integral graphs

Towards a spectral theory of graphs based on the signless Laplacian, III

“…Several infinite families of Q-integral graphs have been constructed in [27] using the join of regular graphs. The formula for the join of regular graphs was derived by the graph divisor technique.…”

“…The divisor technique (see Theorem 2.6 of Part I) has been used in various occasions for computing Q-eigenvalues (see, for example, [27], [36], [51]). …”

“…Reference [27] of Part I was incorrectly given and the correct form reads as here in [40]. [27] is updated reference [24] of Part II. [35] is updated reference [30] of Part II, i.e.…”

“…In the first part of this paper we have mentioned 15 papers (in particular, [4], [6], [10], [15], [20], [22], [23], [35], [39], [41], [43], [44], [46], [47], [55], where the signless Laplacian is used explicitly) in addition to our previous basic papers [5], [9]. In Part II we have added the following 11 references: [1], [3], [24], [25], [26], [27], [34], [36], [48], [52], [54]. In the meantime the following 16 papers [2], [13], [18], [19], [21], [28], [29], [30], [31], [32], [38], [42], [45], [49], [51], [53] have been published or are in the process of publication at this moment.…”

On Q-integral (3,s)-semiregular bipartite graphs

“…On the other hand, the graphs with integral Q-spectrum are studied in [4], [5], [8], [9] and [10], so far. Here we extend those results.…”