完全二部单路图谱半径的极限

The limit of spectral radius of complete bipartite single path-graphs

对于任意给定的正整数r1≥2,r2≥4,r1≤r2,当n→∞时,完全二部单路图G(n,r1,r2)的谱半径ρ(G(n,r1,r2))有极限,即limρn→∞(G(n,r1,r2))=ρ,并确定了极限ρ,即limρn→∞(G(n,r1,r2))=(r2((2+r2r1-2r1)+r2(2+r2r1-2r1)2+4(r2-1)(r1-1)2)^(1/2)/2(r2-1))^(1/2)

For any given integer r1 ≥ 2,r2 ≥ 4,r1 ≤ r2,ρ （ G （ n ,r1 ,r2 ）） the spectral radius of G （ n ,r1 ,r2 ）has limit ρ as n tends to infinite i.e.,limn→∞ρ（ G （ n,r1 ,r2 ））= ρ. we determine the limit limn→∞ρ（G（n,r1,r2））=√r2（2＋r2r1-2r1）＋r2√（2＋r2r1-2r1）^2＋4（r2-1）（r1-1）^2/2（r2-1）