Domination Number of the Non-commuting Graph of Finite Groups

Let G be a non-abelian group. The non-commuting graph of group G, shown by ΓG, is a graph with the vertex set G \ Z(G), where Z(G) is the center of group G. Also two distinct vertices of a and b are adjacent whenever ab ≠ ba. A set S ⊆ V(Γ) of vertices in a graph Γ is a dominating set if every vertex v ∈ V(Γ) is an element of S or adjacent to an element of S. The domination number of a graph Γ denoted by γ(Γ), is the minimum size of a dominating set of Γ. </p><p>Here, we study some properties of the non-commuting graph of some finite groups. In this paper, we show that \gamma(\Gamma_G)<\frac{|G|-|Z(G)|}{2}. Also we charactrize all of groups G of order n with t = ∣Z(G)∣, in which $\gamma(\Gamma_{G})+\gamma(\overline{\Gamma}_{G})\in \{n-t+1,n-t,n-t-1,n-t-2\}.

Dual targeting of TGF-β and PD-L1 inhibits tumor growth in TGF-β/PD-L1-driven colorectal carcinoma

Immunosuppressive factors within the tumor microenvironment (TME), such as Transforming growth factor beta (TGF-β), constitute a crucial hindrance to immunotherapeutic approaches in colorectal cancer (CRC). Furthermore, immune checkpoint factors (e.g., programmed death-ligand 1 [PD-L1]) inhibit T-cell proliferation and activation. To cope with the inhibitory effect of immune checkpoints, the therapeutic value of dual targeting PD-L1 and TGF-β pathways via M7824 plus 5-FU in CRC has been evaluated. Integrative-systems biology approaches and RNAseq were used to assess the differential level of genes associated with 88 metastatic-CRC patients. The level of PD-L1 and TGF-β was evaluated in a validation cohort. The anti-proliferative, migratory, and apoptotic effects of PD-L1/TGF-β inhibitor, M7824, were assessed by MTT, wound-healing assay, and flow cytometry. Anti-tumor activity was assessed in a xenograft model, followed by biochemical studies and histological staining, and gene/protein expression analyses by RT-PCR and ELISA/IHC. The result of differentially expressed genes (DEGs) analysis showed 1268 upregulated and 1074 downregulated genes in CRC patients. Among the highest scoring genes and dysregulated pathways associated with CRC, PD-L1, and TGF-β were identified and further validated in 92 CRC patients. Targeting of PD-L1-TGF-β inhibited cell growth and migration, associated with modulation of CyclinD1 and MMP9. Furthermore, M7824 inhibited tumor growth via targeting TGF-β and PD-L1 pathways, resulting in modulation of inflammatory response and fibrosis via TNF-α/IL6/CD4–8 and COL1A1/1A2, respectively. In conclusion, our data illustrated that co-targeting PD-L1 and TGF-β pathways increased the effect of Fluorouracil (5-FU) and reduced the tumor growth in PD-L1/TGF-β expressing tumors, providing a new therapeutic option in the treatment of CRC.</p