Some families of integral graphs


Wang, Ligong and Broersma, Hajo and Hoede, Cornelis and Li, Xueliang and Still, Georg (2008) Some families of integral graphs. Discrete mathematics, 308 (24). pp. 6383-6391. ISSN 0012-365X

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Abstract:A graph is called integral if all its eigenvalues (of the adjacency matrix) are integers. In this paper, the graphs $K_{1,r}\cdot K_n,\; r^*K_n,\; K_{1,r} \cdot K_{m,n},\; r^*K_{m,n}$ and the tree $K_{1,s}\cdot T(q,r,m,t)$ are defined. We determine the characteristic polynomials of these graphs and also obtain sufficient and necessary conditions for these graphs to be integral. Some sufficient conditions are found by using the number theory and computer search. All these classes are infinite. Some new results which treat interrelations between integral trees of various diameters are also found. The discovery of these integral graphs is a new contribution to the search of such graphs.

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Copyright:© 2008 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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