For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M1(G) = ∑ v∈V (G) dG(v) 2 where dG(v) is the degree of vertex v in G. The alternative expression for M1(G) is ∑ uv∈E(G)(dG(u)+dG(v)). Very recently, Eliasi, Iranmanesh and Gutman [7] introduced a new graphical invariant ∏∗ 1(G) = ∏ uv∈E(G)(dG(u) + dG(v)) as the multiplicative version of ...

A directed triple system of order v, denoted DTS(v), is said to be f-bicyclic if it admits an automorphism consisting of f fixed points and two disjoint cycles. In this paper, we give necessary and sufficient conditions for the existence of f-bicyclic

Bridgehead bicyclic unsaturated enamines were prepared by a tandem rhodium-catalyzed C-H bondactivation/alkenylation/electrocyclization of alkyne-tethered unsaturated imines. These strained bicyclic enamines exhibitunique reactivity: for example, they give N-Alkylated products upon treatment with alkylating reagents and undergo doublebond isomerization to alleviate ring strain upon ...

Among unicyclic digraphs and signed digraphs with fixed number of vertices, the digraphs and signed digraphs with minimal and maximal energy are already determined. In this paper we address the problem of finding bicyclic signed digraphs with extremal energy. We obtain minimal and maximal energy among all those n -vertex bicyclic signed digraphs which contain vertex-disjoint signed directed cyc...

The silyl enol ether derivatives of ketones or esters tethered by a hydrocarbon or ether linkage to the 3-position of a pyridine ring undergo dearomatising nucleophilic attack on the ring once it is activated (as an acylpyridinium species) by the addition of methyl chloroformate. The bicyclic dihydropyridine products are in some cases unstable, but may be isolated after hydrogenation as fused b...

We show that the monoid M2(T) of 2 × 2 tropical matrices is a regular semigroup satisfying the semigroup identity A2B4A2A2B2A2B4A2 =A2B4A2B2A2A2B4A2. Studying reduced identities for subsemigroups of M2(T), and introducing a faithful semigroup representation for the bicyclic monoid by 2 × 2 tropical matrices, we reprove Adjan’s identity for the bicyclic monoid in a much simpler way.

Abstract TIGIT is an emerging immune checkpoint receptor expressed higher than PD-1 in some tumors especially anti-PD1 resistant tumors. By competing with the co-stimulatory CD226/DNAM-1 for binding to CD155/PVR, transduces inhibitory signals and suppresses response. Therefore, we sought discover inhibitors improving tumor immunotherapy. Through directional cloning, bacterial transformation pha...

Доведено, що напівгрупи E n d ( B ω ) та ℤ ендоморфізмів біциклічної розширеної ізоморфні напівпрямим добуткам , + × φ * $ і відповідно.

a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.