The Randić index of a graph G is the sum of (dG(u)dG(v))−1/2 over all edges uv of G, where dG(u) denotes the degree of vertex u in G. In this paper, we investigate a few graph transformations that decrease Randić index of graph. By applying those transformations, we determine the minimum Randić index on tricyclic graphs, and characterize the corresponding extremal graphs.

The syntheses of four novel syn-type tricyclic laddersiloxanes bearing eight or six alkenyl groups are presented. These compounds possess reactive alkenyl groups on both the bridged and side silicon atoms and their structures were determined by characterization using multinuclear NMR spectroscopy, mass spectrometry, and elemental analysis techniques. To investigate their reactivity, compounds were subjected to hydrosilylation using two different silanes, and the resulting fully hydrosilylated compounds were analyzed thoroughly. Remarkably, all the synthesized laddersiloxanes displayed high thermal stability, suggesting their potential as promising precursors for the development of new hybrid materials. Additionally, preliminary findings indicate the possibility of exploiting the reactivity difference between the alkenyl groups attached to the D- and T-unit silicon atoms for the synthesis of Janus molecules. These findings highlight the potential of the reported compounds as valuable building blocks in the construction of innovative materials.

Brucellosis infection induces fever, chills, sweats, headache, myalgia, arthralgia, anorexia, fa-tigue, and mood disorders. In mice, it causes a rise in IL-6, TNF-, and IFN-; and reduces sero-tonin and dopamine levels in hippocampus. There is loss in muscle strength and equilibrium and increased anxiety and hopelessness. Imipramine (ImiP) is a tricyclic antidepressant that increases the capacity of macrophages to destroy intracellular microorganisms in vivo. The effect of ImiP was evaluated in Balb/c mice infected with Brucella abortus 2308. Serum levels were determined in IFN-, IL-6, TNF-, IL-12, MCP-1, and IL-10 by FACS; the bacterial count in the spleen, by CFU; the serotonin concentration in the hippocampus, by HPLC; and strength, equilibrium, and mood by behavioral tests. Our results showed that infected vs. control mice had a significant rise in lev-els of IFN-, IL-6, TNF-, and IL-12 with a low IFN-/IL-6 ratio, elevated bacterial-counts, alter-ations in serotonin concentration at hippocampus, and decreased muscular strength, equilibrium, and mood. Infected mice treated with ImiP vs. infected mice showed: 1) improved mood; 2) in-creased hippocampal serotonin availability, splenic dendritic cells, and macrophage phagocytic activity; and 3) upturn inflammation and reduced CFU ability. Our results support that ImiP fa-vors positive outcomes in subjects handling Brucella infections likely by improving psychoim-mune resilience.