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21.
Akira Hiraki 《Journal of Algebraic Combinatorics》2001,14(2):127-131
Let be a distance-regular graph of diameter d, valency k and r := maxi | (c
i,b
i) = (c
1,b
1). Let q be an integer with r + 1 q d – 1.In this paper we prove the following results:
Theorem 1
Suppose for any pair of vertices at distance q there exists a strongly closed subgraph of diameter q containing them. Then for any integer i with 1 i q
and for any pair of vertices at distance i there exists a strongly closed subgraph of diameter i containing them.
Theorem 2
If r 2, then
c
2r+3 1.As a corollary of Theorem 2 we have d k
2(r + 1) if r 2. 相似文献
22.
Lan Lei Xianya Geng Shuchao Li Yingjun Peng Yuantian Yu 《International journal of quantum chemistry》2019,119(24):e26044
Let denote a molecular graph of linear [n] phenylene with n hexagons and n squares, and let the Möbius phenylene chain be the graph obtained from the by identifying the opposite lateral edges in reversed way. Utilizing the decomposition theorem of the normalized Laplacian characteristic polynomial, we study the normalized Laplacian spectrum of , which consists of the eigenvalues of two symmetric matrices ℒ R and ℒ Q of order 3n. By investigating the relationship between the roots and coefficients of the characteristic polynomials of the two matrices above, we obtain an explicit closed-form formula of the multiplicative degree-Kirchhoff index as well as the number of spanning trees of . Furthermore, we determine the limited value for the quotient of the multiplicative degree-Kirchhoff index and the Gutman index of . 相似文献
23.
We consider random subgraphs of a fixed graph with large minimum degree. We fix a positive integer k and let Gk be the random subgraph where each independently chooses k random neighbors, making kn edges in all. When the minimum degree then Gk is k‐connected w.h.p. for ; Hamiltonian for k sufficiently large. When , then Gk has a cycle of length for . By w.h.p. we mean that the probability of non‐occurrence can be bounded by a function (or ) where . © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 143–157, 2017 相似文献
24.
This paper investigates the topological properties of the Brazilian term structure of interest rates network. We build the minimum spanning tree (MST), which is based on the concept of ultrametricity, using the correlation matrix for interest rates of different maturities. We show that the short-term interest rate is the most important within the interest rates network, which is in line with the Expectation Hypothesis of interest rates. Furthermore, we find that the Brazilian interest rates network forms clusters by maturity. 相似文献
25.
This paper investigates the topological properties of the Brazilian stock market networks. We build the minimum spanning tree, which is based on the concept of ultrametricity, using the correlation matrix for a variety of stocks of different sectors. Our results suggest that stocks tend to cluster by sector. We employ a dynamic approach using complex network measures and find that the relative importance of different sectors within the network varies. The financial, energy and material sectors are the most important within the network. 相似文献
26.
Tomás Feder 《Discrete Mathematics》2008,308(9):1639-1652
A graph is point determining if distinct vertices have distinct neighbourhoods. A realization of a point determining graph H is a point determining graph G such that each vertex-removed subgraph G-x which is point determining, is isomorphic to H. We study the fine structure of point determining graphs, and conclude that every point determining graph has at most two realizations.A full homomorphism of a graph G to a graph H is a vertex mapping f such that for distinct vertices u and v of G, we have uv an edge of G if and only if f(u)f(v) is an edge of H. For a fixed graph H, a full H-colouring of G is a full homomorphism of G to H. A minimal H-obstruction is a graph G which does not admit a full H-colouring, such that each proper induced subgraph of G admits a full H-colouring. We analyse minimal H-obstructions using our results on point determining graphs. We connect the two problems by proving that if H has k vertices, then a graph with k+1 vertices is a minimal H-obstruction if and only if it is a realization of H. We conclude that every minimal H-obstruction has at most k+1 vertices, and there are at most two minimal H-obstructions with k+1 vertices.We also consider full homomorphisms to graphs H in which loops are allowed. If H has ? loops and k vertices without loops, then every minimal H-obstruction has at most (k+1)(?+1) vertices, and, when both k and ? are positive, there is at most one minimal H-obstruction with (k+1)(?+1) vertices.In particular, this yields a finite forbidden subgraph characterization of full H-colourability, for any graph H with loops allowed. 相似文献
27.
A spanning subgraph H of a graph G is a 2-detour subgraph of G if for each x, y ∈ V(G), d
H
(x, y) ≤ d
G
(x, y) + 2. We prove a conjecture of Erdős, Hamburger, Pippert, and Weakley by showing that for some positive constant c and every n, each 2-detour subgraph of the n-dimensional hypercube Q
n
has at least clog2
n · 2
n
edges.
József Balogh: Research supported in part by NSF grants DMS-0302804, DMS-0603769 and DMS-0600303, UIUC Campus Reseach Board
#06139 and #07048, and OTKA 049398.
Alexandr Kostochka: Research supported in part by NSF grants DMS-0400498 and DMS-0650784, and grant 06-01-00694 of the Russian
Foundation for Basic Research. 相似文献
28.
Kenjiro Ogawa 《Discrete Mathematics》2009,309(22):6353-6358
For a poset P=(X,≤P), the double bound graph (DB-graph) of P is the graph DB(P)=(X,EDB(P)), where xy∈EDB(P) if and only if x≠y and there exist n,m∈X such that n≤Px,y≤Pm. We obtain that for a subposet Q of a poset P,Q is an (n, m)-subposet of P if and only if DB(Q) is an induced subgraph DB(P). Using this result, we show some characterizations of split double bound graphs, threshold double bound graphs and difference double bound graphs in terms of (n, m)-subposets and double canonical posets. 相似文献
29.
We study the cross-correlations of buy and sell volumes on the Korean stock market in high frequency. We observe that the pulling effects of volumes are as small as that of returns. The properties of the correlations of buy and sell volumes differ. They are explained by the degree of synchronization of stock volumes. Further, the pulling effects on the minimal spanning tree are studied. In minimal spanning trees with directed links, the large pulling effects are clustered at the center, not uniformly distributed. The Epps effect of buy and sell volumes are observed. The reversal of the cross-correlations of buy and sell volumes is also detected. 相似文献
30.
Simplicial Vertices in Graphs with no Induced Four‐Edge Path or Four‐Edge Antipath,and the H6‐Conjecture 下载免费PDF全文
Let be the class of all graphs with no induced four‐edge path or four‐edge antipath. Hayward and Nastos 6 conjectured that every prime graph in not isomorphic to the cycle of length five is either a split graph or contains a certain useful arrangement of simplicial and antisimplicial vertices. In this article, we give a counterexample to their conjecture, and prove a slightly weaker version. Additionally, applying a result of the first author and Seymour 1 we give a short proof of Fouquet's result 3 on the structure of the subclass of bull‐free graphs contained in . 相似文献