共查询到20条相似文献,搜索用时 31 毫秒
1.
Tam��s Terpai 《Combinatorica》2011,31(6):739-754
Using analytical tools, we prove that for any simple graph G on n vertices and its complement [`(G)]\bar G the inequality $\mu \left( G \right) + \mu \left( {\bar G} \right) \leqslant \tfrac{4}
{3}n - 1$\mu \left( G \right) + \mu \left( {\bar G} \right) \leqslant \tfrac{4}
{3}n - 1 holds, where μ(G) and m( [`(G)] )\mu \left( {\bar G} \right) denote the greatest eigenvalue of adjacency matrix of the graphs G and [`(G)]\bar G respectively. 相似文献
2.
Let
G ì \mathbb C G \subset {\mathbb C} be a finite region bounded by a Jordan curve L: = ?G L: = \partial G , let
W: = \textext[`(G)] \Omega : = {\text{ext}}\bar{G} (with respect to
[`(\mathbb C)] {\overline {\mathbb C}} ), $ \Delta : = \left\{ {z:\left| z \right| > 1} \right\} $ \Delta : = \left\{ {z:\left| z \right| > 1} \right\} , and let w = F(z) w = \Phi (z) be a univalent conformal mapping of Ω onto Δ normalized by $ \Phi \left( \infty \right) = \infty, \;\Phi '\left( \infty \right) > 0 $ \Phi \left( \infty \right) = \infty, \;\Phi '\left( \infty \right) > 0 . By A
p
(G); p > 0; we denote a class of functions f analytic in G and satisfying the condition
|| f ||App(G): = òG | f(z) |pdsz < ¥, \left\| f \right\|_{Ap}^p(G): = \int\limits_G {{{\left| {f(z)} \right|}^p}d{\sigma_z} < \infty, } 相似文献
3.
Suppose G is a transitive permutation group on a finite set W\mit\Omega of n points and let p be a prime divisor of |G||G|. The smallest number of points moved by a non-identity p-element is called the minimal p-degree of G and is denoted mp (G). ¶ In the article the minimal p-degrees of various 2-transitive permutation groups are calculated. Using the classification of finite 2-transitive permutation groups these results yield the main theorem, that mp(G) 3 [(p-1)/(p+1)] ·|W|m_{p}(G) \geq {{p-1} \over {p+1}} \cdot |\mit\Omega | holds, if Alt(W) \nleqq G {\rm Alt}(\mit\Omega ) \nleqq G .¶Also all groups G (and prime divisors p of |G||G|) for which mp(G) £ [(p-1)/(p)] ·|W|m_{p}(G)\le {{p-1}\over{p}} \cdot |\mit\Omega | are identified. 相似文献
4.
Kewen Zhao 《Monatshefte für Mathematik》2009,20(1):279-293
Let G be a simple graph with n vertices. For any v ? V(G){v \in V(G)} , let N(v)={u ? V(G): uv ? E(G)}{N(v)=\{u \in V(G): uv \in E(G)\}} , NC(G) = min{|N(u) èN(v)|: u, v ? V(G){NC(G)= \min \{|N(u) \cup N(v)|: u, v \in V(G)} and
uv \not ? E(G)}{uv \not \in E(G)\}} , and NC2(G) = min{|N(u) èN(v)|: u, v ? V(G){NC_2(G)= \min\{|N(u) \cup N(v)|: u, v \in V(G)} and u and v has distance 2 in E(G)}. Let l ≥ 1 be an integer. A graph G on n ≥ l vertices is [l, n]-pan-connected if for any u, v ? V(G){u, v \in V(G)} , and any integer m with l ≤ m ≤ n, G has a (u, v)-path of length m. In 1998, Wei and Zhu (Graphs Combinatorics 14:263–274, 1998) proved that for a three-connected graph on n ≥ 7 vertices, if NC(G) ≥ n − δ(G) + 1, then G is [6, n]-pan-connected. They conjectured that such graphs should be [5, n]-pan-connected. In this paper, we prove that for a three-connected graph on n ≥ 7 vertices, if NC
2(G) ≥ n − δ(G) + 1, then G is [5, n]-pan-connected. Consequently, the conjecture of Wei and Zhu is proved as NC
2(G) ≥ NC(G). Furthermore, we show that the lower bound is best possible and characterize all 2-connected graphs with NC
2(G) ≥ n − δ(G) + 1 which are not [4, n]-pan-connected. 相似文献
5.
An edge coloring is called vertex-distinguishing if every two distinct vertices are incident to different sets of colored edges. The minimum number of colors required for
a vertex-distinguishing proper edge coloring of a simple graph G is denoted by c¢vd(G){\chi'_{vd}(G)}. It is proved that c¢vd(G) £ D(G)+5{\chi'_{vd}(G)\leq\Delta(G)+5} if G is a connected graph of order n ≥ 3 and
s2(G) 3 \frac2n3{\sigma_{2}(G)\geq\frac{2n}{3}}, where σ
2(G) denotes the minimum degree sum of two nonadjacent vertices in G. 相似文献
6.
For a simple connected undirected graph G, c(G), cf(G), Yf(G), f(G), ?G(G){\chi(G), \chi_f(G), \Psi_f(G), \phi(G), \partial \Gamma (G)} and Ψ(G) denote respectively the chromatic number, fall chromatic number (assuming that it exists for G), fall achromatic number, b-chromatic number, partial Grundy number and achromatic number of G. It is shown in Dunbar et al. (J Combin Math & Combin Comput 33:257–273, 2000) that for any graph G for which fall coloring exists, c(G) £ cf(G) £ Yf (G) £ f(G) £ ?G(G) £ Y(G){\chi (G)\leq \chi_f(G) \leq \Psi_f (G) \leq \phi(G) \leq \partial \Gamma (G)\leq \Psi (G)} . In this paper, we exhibit an infinite family of graphs G with a strictly increasing color chain: c(G) < cf(G) < Yf (G) < f(G) < ?G(G) < Y(G){\chi (G) < \chi_f(G) < \Psi_f (G) < \phi(G) < \partial \Gamma (G) < \Psi (G)} . The existence of such a chain was raised by Dunbar et al. 相似文献
7.
A Roman dominating function on a graph G = (V, E) is a function f : V ? {0, 1, 2}f : V \rightarrow \{0, 1, 2\} satisfying the condition that every vertex v for which f(v) = 0 is adjacent to at least one vertex u for which f(u) = 2. The weight of a Roman dominating function is the value w(f) = ?v ? V f(v)w(f) = \sum_{v\in V} f(v). The Roman domination number of a graph G, denoted by gR(G)_{\gamma R}(G), equals the minimum weight of a Roman dominating function on G. The Roman domination subdivision number sdgR(G)sd_{\gamma R}(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the Roman domination number. In this paper, first we establish upper
bounds on the Roman domination subdivision number for arbitrary graphs in terms of vertex degree. Then we present several
different conditions on G which are sufficient to imply that $1 \leq sd_{\gamma R}(G)
\leq 3$1 \leq sd_{\gamma R}(G)
\leq 3. Finally, we show that the Roman domination subdivision number of a graph can be arbitrarily large. 相似文献
8.
D. S. Malyshev 《Journal of Applied and Industrial Mathematics》2012,6(1):97-99
Under study is the complexity status of the independent set problem in a class of connected graphs that are defined by functional
constraints on the number of edges depending on the number of vertices. For every natural number C, this problem is shown to be polynomially solvable in the class of graphs
|