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The zeroth-order general Randi\'{c} index of graphs with a given clique number
Jianwei Du,Yanling Shao,Xiaoling Sun 강원경기수학회 2020 한국수학논문집 Vol.28 No.3
The zeroth-order general Randi\'{c} index $^{0}R_{\alpha}(G)$ of the graph $G$ is defined as $\sum_{u\in V(G)}d(u)^{\alpha}$, where $d(u)$ is the degree of vertex $u$ and $\alpha$ is an arbitrary real number. In this paper, the maximum value of zeroth-order general Randi\'{c} index on the graphs of order $n$ with a given clique number is presented for any $\alpha\neq 0,1$ and $\alpha \notin (2,2n-1]$, where $n=|V(G)|$. The minimum value of zeroth-order general Randi\'{c} index on the graphs with a given clique number is also obtained for any $\alpha\neq 0,1$. Furthermore, the corresponding extremal graphs are characterized.
TIGHT UPPER BOUND ON THE EXPONENTS OF A CLASS OF TWO-COLORED DIGRAPHS
Wang, Rong,Shao, Yanling,Gao, Yubin Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
A two-colored digraph D is primitive if there exist nonnegative integers hand k with h + k > 0 such that for each pair (i, j) of vertices there exists an (h, k)-walk in D from i to j. The exponent of the primitive two-colored digraph D is the minimum value of h + k taken over all such hand k. In this paper, we give the tight upper bound on the exponents of a class of primitive two-colored digraphs with (s + 1) n-cycles and one (n - 1)-cycle, and the characterizations of the extremal two-colored digraphs.
Tight upper bound on the exponents of a class of two-colored digraphs
Rong Wang,Yanling Shao,Yubin Gao 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
A two-colored digraph D is primitive if there exist nonnegative integers h and k with h + k > 0 such that for each pair (i, j) of vertices there exists an (h, k)-walk in D from i to j. The exponent of the primitive two-colored digraph D is the minimum value of h + k taken over all such h and k. In this paper, we give the tight upper bound on the exponents of a class of primitive two-colored digraphs with (s + 1) n−cycles and one (n − 1)−cycle, and the characterizations of the extremal two-colored digraphs.
Nanotherapeutics with immunoregulatory functions for the treatment of bacterial infection
Dongliang Yang,Meng Ding,Yanni Song,Yanling Hu,Weijun Xiu,Lihui Yuwen,Yannan Xie,Yingnan Song,Jinjun Shao,Xuejiao Song,Heng Dong 한국생체재료학회 2023 생체재료학회지 Vol.27 No.00
The advent of drug-resistant pathogens results in the occurrence of stubborn bacterial infections that cannot betreated with traditional antibiotics. Antibacterial immunotherapy by reviving or activating the body’s immune systemto eliminate pathogenic bacteria has confrmed promising therapeutic strategies in controlling bacterial infections. Subsequent studies found that antimicrobial immunotherapy has its own benefts and limitations, such as avoidingrecurrence of infection and autoimmunity-induced side efects. Current studies indicate that the various antibacterialtherapeutic strategies inducing immune regulation can achieve superior therapeutic efcacy compared with mono therapy alone. Therefore, summarizing the recent advances in nanomedicine with immunomodulatory functionsfor combating bacterial infections is necessary. Herein, we briefy introduce the crisis caused by drug-resistantbacteria and the opportunity for antibacterial immunotherapy. Then, immune-involved multimodal antibacterialtherapy for the treatment of infectious diseases was systematically summarized. Finally, the prospects and challengesof immune-involved combinational therapy are discussed.