Wang, Ligong; Hoede, Cornelis

Constructing fifteen infinite classes of nonregular bipartite integral graphs

Electron. J. Comb. 15(1), Research Paper R8, 29 p. (2008)


Summary: A graph is called integral if all its eigenvalues (of the adjacency matrix) are integers. In this paper, the graphs $S1(t) = K1,t, S2(n, t), S3(m, n, t), S4(m, n, p, q), S5(m, n), S6(m, n, t), S8(m, n), S9(m, n, p, q), S10(n), S13(m, n), S17(m, n, p, q), S18(n, p, q, t), S19(m, n, p, t), S20(n, p, q)$ and $S21(m, t)$ are defined. We construct the fifteen classes of larger graphs from the known 15 smaller integral graphs S1 - S6, S8 - S10, S13, S17 - S21 (see also Figures 4 and 5, Bali$\acute $nska and Simi$\acute c$, Discrete Math. $236(2001) 13$-24). These classes consist of nonregular and bipartite graphs.

Mathematics Subject Classification

05C50, 11D09, 11D41