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共查询到16条相似文献，搜索用时 187 毫秒
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$G$是一个阶为$n$围长为$g$的简单图, $u$和$v$是$G$中任意两个相邻顶点, 如果$d_{G}(u)$ + $d_{G}(v)$ $\geq$ $n - 2g + 5$, 则$G$是上可嵌入的; 如果$G$是2-\!边连通(或3-\!边连通)图, 则当 $d_{G}(u)$ + $d_{G}(v)$ $\geq$ $n - 2g + 3$ (或 $d_{G}(u)$ + $d_{G}(v)$ $\geq$ $n - 2g - 5$)时$G$是上可嵌入的, 并且上面3个下界都是紧的.  相似文献

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The induced matching cover number of a graph G without isolated vertices, denoted by imc（G）, is the minimum integer k such that G has k induced matchings M1, M2,..., Mk such that, M1∪M2∪…∪Mk covers V（G）. This paper shows if G is a nontrivial tree, then imc（G） E {△0^＊CG）, △0^＊（G） ＋ 1, △0^＊（G） ＋ 2}, where △0^＊（G） = max{d0（u） ＋ d0（v）： u,v ∈ V（G）,uv ∈ E（G）}.  相似文献

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The Balaban index of a connected graph G is defined as J(G) =|E(G)|μ + 1∑e=uv∈E(G)1√DG(u)DG(v),and the Sum-Balaban index is defined as SJ(G) =|E(G)|μ + 1∑e=uv∈E(G)1√DG(u)+DG(v),where DG(u) =∑w∈V(G)dG(u, w), and μ is the cyclomatic number of G. In this paper, the unicyclic graphs with the maximum Balaban index and the maximum Sum-Balaban index among all unicyclic graphs on n vertices are characterized, respectively.  相似文献

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Let G = （V, E） be a simple connected graph, and ｜V（G）｜ ≥ 2. Let f be a mapping from V（G） ∪ E（G） to {1,2…, k}. If arbitary uv ∈ E（G）,f（u） ≠ f（v）,f（u） ≠ f（uv）,f（v） ≠ f（uv）; arbitary uv, uw ∈ E（G）（v ≠ w）, f（uv） ≠ f（uw）;arbitary uv ∈ E（G） and u ≠ v, C（u） ≠ C（v）, where
C（u）={f（u）}∪{f（uv）｜uv∈E（G）}.
Then f is called a k-adjacent-vertex-distinguishing-proper-total coloring of the graph G（k-AVDTC of G for short）. The number min{k｜k-AVDTC of G} is called the adjacent vertex-distinguishing total chromatic number and denoted by χat（G）. In this paper we prove that if △（G） is at least a particular constant and δ ≥32√△ln△, then χat（G） ≤ △（G） ＋ 10^26 ＋ 2√△ln△.  相似文献

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Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui ： i = 1, 2 , m}. Let κ = ec＋1. Forj = 1,2,...,k- 1, let δij = max{dv ： dist（v, ui） = j,v ∈ Ti}, δj = max{δij ： i = 1, 2,..., m}, δ0 = max{dui ： ui ∈ V（Cm）}. Then λ1（G）≤max{max 2≤j≤k-2 （√δj-1-1＋√δj-1）,2＋√δ0-2,√δ0-2＋√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 （G） is the largest eigenvalue of the adjacency matrix of G.  相似文献

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Let G = （V,E） be a graph.A function f ： E → {-1,1} is said to be a signed edge total dominating function （SETDF） of G if e ∈N（e） f（e ） ≥ 1 holds for every edge e ∈ E（G）.The signed edge total domination number γ st （G） of G is defined as γ st （G） = min{ e∈E（G） f（e）｜f is an SETDF of G}.In this paper we obtain some new lower bounds of γ st （G）.  相似文献

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Let G be a finite group and p be a fixed prime. A p-Brauer character of G is said to be monomial if it is induced from a linear p-Brauer character of some subgroup(not necessarily proper) of G. Denote by IBr_m(G) the set of irreducible monomial p-Brauer′characters of G. Let H = G′O~p′(G) be the smallest normal subgroup such that G/H is an abelian p′-group. Suppose that g ∈ G is a p-regular element and the order of gH in the factor group G/H does not divide |IBr_m(G)|. Then there exists ? ∈ IBr_m(G) such that ?(g) = 0.  相似文献