A neighbor full sum distinguishing total coloring of a graph G is a proper total coloring ϕ such that no two adjacent vertices u and v of G satisfy ω (u)=ω (v) , where for any v ∈ V(G) , ω (v)=ϕ (v)+∑ _e∋ vϕ (e)+∑ _u∈ N(v)ϕ (u) and N(v) = {u ∈ V(G) | uv ∈ E(G)} . The minimum number of colors required for the coloring is called neighbor full sum distinguishing total chromatic number, denoted by ftndi_Σ (G) . In this paper, we show that ftndi_Σ (G) ≤Δ (G)+3 if G is a normal planar graph with girth g(G)≥ 6 and maximum degree Δ (G) ≥ 10 .
Let T be a connected subgraph of a graph G, the T-structure connectivity kappa(G;T) (resp. T-substructure connectivity kappa s(G;T)) of G is the minimum cardinality of a set of subgraphs F of G that each is isomorphic to T (resp. a connected subgraph of T) such that G-F is disconnected or a singleton. The n-dimensional folded locally twisted cube, FLTQn, is a graph, which is obtained by adding edges to n-dimensional locally twisted cube, LTQn. In this paper, we study star- and cycle-structures connectivity and substructures connectivity of FLTQn. We get that star (K1,m)-structure (substructure) connectivity of FLTQn is 2 <= m <= n2. Furthermore, we calculate kappa(FLTQn;C2k)=n+1k for 3 <= k <= n.
Given a planar graph H, let f(& Bernoullis;& Pscr;)(n,H) denote the maximum number of copies of H in a bipartite planar graph on n vertices. Let Pk denote the path on k vertices. In this paper, we determine the exact value of f(& Bernoullis;& Pscr;)(n, P-k) and characterize all bipartite planar graphs containing f(& Bernoullis;& Pscr;) (n, P-k) copies of P-k for each k is an element of {3, 4, 5}. In addition, we give a conjecture of asymptotic value of f(& Bernoullis;& Pscr;)(n, Pk) for all k >= 6. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The optimal barrier dividend problem under excess of loss reinsurance strategy has rarely been studied so far. We combine the risk factors such as market friction and terminal residual value with risk investment and risk control strategy, and study the resulting optimal investment-excess of loss reinsurance-barrier dividend problem. Based on the dynamic programming principle, we establish the Hamilton-Jacobi-Bellman equation, and obtain the explicit solutions for the optimal investment-excess of loss reinsurance strategy. The optimal dividend function is solved by the differential-integral method. The existence and uniqueness of the optimal dividend boundary is proved.
乳腺癌是最常见的肿瘤之一,其治疗仍有很大的改进空间.拓扑异构酶Ⅱ α是治疗乳腺癌等人类疾病的潜在靶点.天然产物具有广泛的生物学活性和化学骨架代表性,是新药发现的重要源泉.使用Autodock vina对天然产物数据库IBScreen NP进行了基于分子对接的虚拟筛选.根据它们的打分值和结构多样性筛查,对获得的22个命中化合物进行体外pBR322 DNA松弛实验验证.结果显示,候选化合物4(CP4)对拓扑异构酶Ⅱα的抑制效果最好.体外抗肿瘤活性结果表明,CP4有一定的抗乳腺癌活性.
