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101.
The energy of graphs and matrices 总被引:1,自引:0,他引:1
Vladimir Nikiforov 《Journal of Mathematical Analysis and Applications》2007,326(2):1472-1475
102.
F. Jaeger has shown that up to a ± sign the evaluation at (j, j
2) of the Tutte polynomial of a ternary matroid can be expressed in terms of the dimension of the bicycle space of a representation over GF(3). We give a short algebraic proof of this result, which moreover yields the exact value of ±, a problem left open in Jaeger's paper. It follows that the computation of t(j, j
2) is of polynomial complexity for a ternary matroid.E. Gioan: C.N.R.S., MontpellierM. Las Vergnas: C.N.R.S., Paris 相似文献
103.
树上秘密共享体制的信息率 总被引:1,自引:0,他引:1
研究以树G为通道结构的秘密共享体制的最优信息率ρ(G)。得到了ρ(G)=2/3的要条件。证明了ρ(G)不会介于实数区间(3/5,2/3)中,给出了以树G的阶数表示的ρ(G)的下界,求出两类具有某种结构的树的最优信息率。 相似文献
104.
Let G be a graph on n vertices with vertex connectivity v with 1 ≤ v ≤ n -2. We produce an attainable upper bound on the absolute algebraic connectivity of G in terms of n and v . 相似文献
105.
The slope-number of a graph G is the minimum number of distinct edge slopes in a straight-line drawing of G in the plane. We prove that for Δ5 and all large n, there is a Δ-regular n-vertex graph with slope-number at least . This is the best known lower bound on the slope-number of a graph with bounded degree. We prove upper and lower bounds on the slope-number of complete bipartite graphs. We prove a general upper bound on the slope-number of an arbitrary graph in terms of its bandwidth. It follows that the slope-number of interval graphs, cocomparability graphs, and AT-free graphs is at most a function of the maximum degree. We prove that graphs of bounded degree and bounded treewidth have slope-number at most . Finally we prove that every graph has a drawing with one bend per edge, in which the number of slopes is at most one more than the maximum degree. In a companion paper, planar drawings of graphs with few slopes are also considered. 相似文献
106.
The independence polynomial, ω(G,x)=∑wkxk, of a graph, G, has coefficients, wk, that enumerate the ways of selecting k vertices from G so that no two selected vertices share an edge. The independence number of G is the largest value of k for which wk≠0. Little is known of less straightforward relationships between graph structure and the properties of ω(G,x), in part because of the difficulty of calculating values of wk for specific graphs. This study presents a new algorithm for these calculations which is both faster than existing ones and easily adaptable to high-level computer languages. 相似文献
107.
Two graphs G1 and G2 of order n pack if there exist injective mappings of their vertex sets into [n], such that the images of the edge sets do not intersect. Sauer and Spencer proved that if Δ (G1) Δ (G2) < 0.5n, then G1 and G2 pack.
In this note, we study an Ore-type analogue of the Sauer–Spencer Theorem. Let θ(G) = max{d(u) + d(v): uv∈E(G)}. We show that if θ(G1)Δ(G2) < n, then G1 and G2 pack. We also characterize the pairs (G1,G2) of n-vertex graphs satisfying θ(G1)Δ(G2) = n that do not pack.
This work was supported in part by NSF grant DMS-0400498. The work of the first author was also partly supported by grant
05-01-00816 of the Russian Foundation for Basic Research. 相似文献
108.
We introduce a generalized dot product and provide some embedding conditions under which the genus of a graph does not rise
under a dot product with the Petersen graph. Using these conditions, we disprove a conjecture of Tinsley and Watkins on the
genus of dot products of the Petersen graph and show that both Grünbaum’s Conjecture and the Berge-Fulkerson Conjecture hold
for certain infinite families of snarks. Additionally, we determine the orientable genus of four known snarks and two known
snark families, construct a new example of an infinite family of snarks on the torus, and construct ten new examples of infinite
families of snarks on the 2-holed torus; these last constructions allow us to show that there are genus-2 snarks of every
even order n ≥ 18. 相似文献
109.
Max Forester 《Geometriae Dedicata》2006,121(1):43-59
We study the structure of generalized Baumslag–Solitar groups from the point of view of their (usually non-unique) splittings
as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity
(fully reduced decompositions) and give a simplified proof of the existence of deformations. We also prove a finiteness theorem and solve
the isomorphism problem for generalized Baumslag–Solitar groups with no non-trivial integral moduli.
相似文献
110.
连通的顶点可迁图的色唯一性 总被引:3,自引:0,他引:3
本文给出从一个已知的顶点可迁的非色唯一图出发,构造无穷多个顶点可迁的非色唯一图的一种方法,据此给出若干类无穷多个连通的顶点可迁,但不是色唯一的图簇,从而进一步否定地回答了Chia在[1]中提出的问题. 相似文献