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31.
32.
Mirko Lepović 《Journal of Applied Mathematics and Computing》2003,11(1-2):109-122
A tree is called starlike if it has exactly one vertex of degree greater than two. In [4] it was proved that two starlike treesG andH are cospectral if and only if they are isomorphic. We prove here that there exist no two non-isomorphic Laplacian cospectral starlike trees. Further, letG be a simple graph of ordern with vertex setV(G)={1,2, …,n} and letH={H 1,H 2, ...H n } be a family of rooted graphs. According to [2], the rooted productG(H) is the graph obtained by identifying the root ofH i with thei-th vertex ofG. In particular, ifH is the family of the paths $P_{k_1 } , P_{k_2 } , ..., P_{k_n } $ with the rooted vertices of degree one, in this paper the corresponding graphG(H) is called the sunlike graph and is denoted byG(k 1,k 2, …,k n ). For any (x 1,x 2, …,x n ) ∈I * n , whereI *={0,1}, letG(x 1,x 2, …,x n ) be the subgraph ofG which is obtained by deleting the verticesi 1, i2, …,i j ∈ V(G) (0≤j≤n), provided that $x_{i_1 } = x_{i_2 } = ... = x_{i_j } = 0$ . LetG(x 1,x 2,…, x n] be the characteristic polynomial ofG(x 1,x 2,…, x n ), understanding thatG[0, 0, …, 0] ≡ 1. We prove that $$G[k_1 , k_2 ,..., k_n ] = \Sigma _{x \in ^{I_ * ^n } } \left[ {\Pi _{i = 1}^n P_{k_i + x_i - 2} (\lambda )} \right]( - 1)^{n - (\mathop \Sigma \limits_{i = 1}^n x_i )} G[x_1 , x_2 , ..., x_n ]$$ where x=(x 1,x 2,…,x n );G[k 1,k 2,…,k n ] andP n (γ) denote the characteristic polynomial ofG(k 1,k 2,…,k n ) andP n , respectively. Besides, ifG is a graph with λ1(G)≥1 we show that λ1(G)≤λ1(G(k 1,k 2, ...,k n )) < for all positive integersk 1,k 2,…,k n , where λ1 denotes the largest eigenvalue. 相似文献
33.
Mega MS Allegrini P Grigolini P Latora V Palatella L Rapisarda A Vinciguerra S 《Physical review letters》2003,90(18):188501
We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent mu=2.06+/-0.01. We propose the long-range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes. 相似文献
34.
Let G be a simple graph and let ¯G denote its complement. A graph G is said to be integral if its spectrum contains integral values. If
is integral with >1 and a>b, where mG denotes the m-fold union of the graph G, we show that it belongs to the class of integral graphs
where (i) (kn
2
s
2+km
nst+ms,km
2
t
2+kmnst+ms)= such that (m,)=1 and (s,)=1; (ii) k,m,n,s,t,z such that (k,m)=1, (k,s)=1, (m,n)=1, (m,s)=1, (n,t)=1 and (s,t)=1; and (iii) ns>m
t.
Acknowledgments.The author is very grateful to the referees for their valuable comments and suggestions concerning this paper.1991 Mathematics Subject Classification. 05 C 50 相似文献
35.
Mirko Degli Esposti Stefano Isola Andreas Knauf 《Communications in Mathematical Physics》2007,275(2):297-329
We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter
is not uniformly expanding. Each map being composed of two fractional linear transformations, the family generalizes many
particular properties which for the case of the Farey map have been successfully exploited in number theory. We analyze the
dynamics through the spectral properties of the generalized transfer operator. Application of the thermodynamic formalism
to the family reveals first and second order phase transitions and unusual properties like positivity of the interaction function. 相似文献
36.
37.
Mirko Horňák 《Discrete Mathematics》2008,308(7):1268-1281
A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ; from a result by Barth and Fournier it follows that Δ(T)?4. A necessary and a sufficient condition for being an arbitrarily vertex decomposable star-like tree have been exhibited. The conditions seem to be very close to each other. 相似文献
38.
The periodic risk model with investment 总被引:1,自引:0,他引:1
We consider a periodic risk model with the possibility of investing into a risky asset, given by a geometrical Brownian motion. The aim is to maximize the adjustment coefficient of the risk process. It is shown that the optimal investment strategy only depends on the averaged data of the model and is constant over time. Thus maximizing the adjustment coefficient is a very weak optimization criterion. 相似文献
39.
40.