... that di= 2 = dj; hencethere are 2a − 2 edges i ∼ j such that di= 2 and dj= 3 and3n−5a +2 2 edges i ∼ j with di= 3 = dj= 3. We then find thati∼jdidj= 27 n 21 a +2 2andi∼j(di+dj 2) ... combinatorics 15 (20 08), #R 120 22 (2) ,3(3)0,1 ,44A3A 2 A1A(3),5 (2) ,4(3)0,1 ,2 (4),5(5)0 ,2 (2) ,5 (2) 0 ,2, 3(3),5(3)Figure 3: 3-regular, non-bipartite, Laplacian integral graphs 3 Structural ... ,4,50,1(3) ,2 0,1(5),3(5),5(4)D4D5D6D7D8D9 (2) (2) ,3 (2) ,4,5(3)0,1 (2) ,4 (2) ,5 (2) ,2, 3(4)0,1 (2) ,2 (3),4 (2) ,5(4) (3)Figure 5: connected, non-regular, Laplacian integral graphs with maximum degree 3the...