Some families of integral graphs

Ligong Wang, Haitze J. Broersma, C. Hoede, Xueliang Li, Xueliang Li, Georg J. Still

3 Citations (Scopus)

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.
Original language English 10.1016/j.disc.2007.12.010 6383-6391 9 Discrete mathematics 308 WoTUG-31/24 https://doi.org/10.1016/j.disc.2007.12.010 Published - Dec 2008

Keywords

• EWI-14551
• Spectrum
• Integral tree
• Integral graph
• General Pell’s equation
• IR-62590
• METIS-254963