A disjoint union of complete graphs is in general not determined by its Laplacian spectrum. It is shown in this paper that if one only considers the family of graphs without isolated vertex, then a disjoint union of complete graphs is determined by its Laplacian spectrum within this family. Moreover, it is shown that the disjoint union of two complete graphs with a and b vertices, a b > 5 3 and...

A dumbbell graph, denoted by Da,b,c, is a bicyclic graph consisting of two vertexdisjoint cycles Ca, Cb and a path Pc+3 (c > −1) joining them having only its end-vertices in common with the two cycles. In this paper, we study the spectral characterization w.r.t. the adjacency spectrum of Da,b,0 (without cycles C4) with gcd(a, b) > 3, and we complete the research started in [J.F. Wang et al., A ...

The 70.6.MHz IrB NMR spectrum of 1,2-B,,C,H,z has been assigned by use of labeled derivatives. The assignments are, in order of increasing field, B(9,12), B(8,10), B(4,5,7,! 1) and B(3,6). Resonances in 1,7-B&H,, are due, in order of increasing field, to B(S,12), B(9,10), B(4,6,8,11) and B(2,3). The ‘H NMR spectrum of 1,2-D,-1,2B,,C,H,, in C,D, contains four quartets at -2.7, -2.5. -2.1, and -1...