Let  be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset  is a minimum neighborhood dominating set if  is a dominating set and if for every  holds. The minimum cardinality of the minimum neighborhood dominating set of a graph  is called as minimum neighborhood dominating number and it is denoted by  . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the

    Synthesis of 2-mercaptobenzothiazole (A₁) is performed from the reaction of  o-aminothiophenol and carbon disulfide CS₂ in ethanol under basic condition. Compound (A₁)  is reacted with chloro acetyl chloride to give compound (A₂). Hydrazide acid compound (A₃) is obtained from the reaction of compound (A₂) with  hydrazine hydrate in ethanol under reflux in the presence of glacial acetic acid .The reaction of hydrazide acid compound (A₃) with ethyl acetoacetate gives pyrazole compound (A₄). The new hydrazone  compound (A₅) was prepared from the reaction of compound (A₃) with  benzaldehyde. Reaction of compound

Derivatives of Schiff-bases possess a great importance in pharmaceutical chemistry. They can be used for synthesizing different types of bioactive compounds. In this paper, derivatives of new Schiff bases have been synthesized from several serial steps. The acid (I) was synthesized from the reaction of dichloroethanoic acid with 2 moles of p-aminoacetanilide. New acid (I) converted to its ester (II) via the reaction of (I) with dimethyl sulphate in the present of anhydrous of sodium carbonate and dry acetone. Acid hydrazide (III) has been synthesized by adding 80% of hydrazine hydrate  to the new ester using ethanol as a solvent. The last step included the preparation of new Schiff-bases (IV-VIII) by the reaction of acid hydrazide with

Indexes of topological play a crucial role in mathematical chemistry and network theory, providing valuable insights into the structural properties of graphs. In this study, we investigate the Resize graph of G2(3), a significant algebraic structure arising from the exceptional Lie group (G2) over the finite field F3. We compute several well-known topological indices, including the Zagreb indices, Wiener index, and Randić index, to analyze the graph's connectivity and complexity. Our results reveal intricate relationships between the algebraic structure of G2(3) and its graphical properties, offering a deeper understanding of its combinatorial and spectral characteristics. These findings contribute to the broader study of algebraic graph t

A new type of the connected domination parameters called tadpole domination number of a graph is introduced. Tadpole domination number for some standard graphs is determined, and some bounds for this number are obtained. Additionally, a new graph, finite, simple, undirected and connected, is introduced named weaver graph. Tadpole domination is calculated for this graph with other families of graphs.

The aim of this article is to introduce a new definition of domination number in graphs called hn-domination number denoted by . This paper presents some properties which show the concepts of connected and independent hn-domination. Furthermore, some bounds of these parameters are determined, specifically, the impact on hn-domination parameter is studied thoroughly in this paper when a graph is modified by deleting or adding a vertex or deleting an edge.

Synthesis of a new class of Schiff-base ligand with a tetrazole moiety to form polymeric metal complexes with Co^II, Ni^II, Zn^II, and Cd^II ions has been demonstrated. The ligand was synthesised by a multi-steps by treating 5-amino-2-chlorobenzonitrile and cyclohexane -1,3-dione, the 5,5'-(((1E,3E)-cyclohexane-1,3-diylidene)bis(azanylylidene))bis(2-chlorobenzonitrile) was obtained. The precursor (M) was prepared  from the reaction 5,5'-(((1E,3E)-cyclohexane-1,3-diylidene)bis(azanylylidene))bis(2-chlorobenzonitrile) with NaN₃ to obtained (1E,3E)-N¹,N³-bis(4-chloro-3-(1H-tetrazol-5-yl)phenyl)cyclohexane-1,3-diimine (N). By reacting the precursor (M) with CS₂

Graph  is a tool that can be used to simplify and solve network problems. Domination is a typical network problem that graph theory is well suited for. A subset of nodes in any network is called dominating if every node is contained in this subset, or is connected to a node in it via an edge. Because of the importance of domination in different areas, variant types of domination have been introduced according to the purpose they are used for. In this paper, two domination parameters the first is the restrained and the second is secure domination have been chosn. The secure domination, and some types of restrained domination in one type of trees is called complete ary tree  are determined.

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This search includes the preparation of Schiff base ligand (SB) from condensation primary amine with vanillin. The new ligand was diagnosed by spectroscopic methods as Mass, NMR, CHN and FTIR. Ligand complexes were mixed from new (SB) and Anthranillic acid (A) with five metal (II) chlorides. The preparation and diagnosis were conducted by FTIR, CHN, UV-visible, molar conductivity, atomic absorption and magnetic moment. The octahedral geometrical shape of the complexes was proposed. The ligands and their new complexes were screened with two different types of bacteria.