Maximal Domination and Maximal Total Domination in Digraphs

ABSTRACT Let D=(V, A) be a digraph. A dominating set S of a digraph D is a maximal dominating set if V -S is not a dominating set of D. The maximal domination number m (D) of D is minimum cardinality of a maximal dominating set of D. A total dominating set S of a digraph D is a maximal total dominating set if V -S is not a total dominating set of D. The maximal total domination number mt (D) of D is the minimum cardinality of a maximal total dominating set of D. In this paper, we initiate a study of maximal domination and maximal total domination in digraphs and obtain some results on these two parameters. Mathematics Subject Classification: 05C

Multiplicative Product Connectivity and Sum Connectivity Indices of Chemical Structures in Drugs

In Chemical sciences, the multiplicative connectivity indices are used in the analysis of drug molecular structures which are helpful for chemical and medical scientists to find out the chemical and biological characteristics of drugs. In this paper, we compute the multiplicative product and sum connectivity indices of some important nanostar dendrimers which appeared in nanoscience

Certain topological indices and related polynomials for polysaccharides

A polysaccharide is a large molecule made of many smaller monosaccharides. Monosaccharides are simple sugars, like glucose. Special enzymes bind these small monomers together creating large sugar polymers or polysaccharides. A polysaccharide is also called a glycan. Starch, glycogen, and cellulose are examples of polysaccharides. Depending on their structure, polysaccharides can have a wide variety of functions in nature. Some polysaccharides are used for storing energy, some for sending cellular messages, and others for providing support to cells and tissues. In the present work, we focus on the polysaccharides, namely, amylose and blue starch-iodine complex. Several topological indices and polynomials are determined in view of edge dividing methods. Also, depict their graphic behavior.Publisher's Versio

Equitable total domination in graphs

A subset ‫ܦ‬ of a vertex set ܸሺ‫ܩ‬ሻ of a graph ‫ܩ‬ ൌ ሺܸ, ‫ܧ‬ሻ is called an equitable dominating set if for every vertex ‫ݒ‬ ‫א‬ ܸ െ ‫ܦ‬ there exists a vertex ‫ݑ‬ ‫א‬ ‫ܦ‬ such that ‫ݒݑ‬ ‫א‬ ‫ܧ‬ሺ‫ܩ‬ሻ and |݀݁݃ሺ‫ݑ‬ሻ െ ݀݁݃ሺ‫ݒ‬ሻ| 1, where ݀݁݃ሺ‫ݑ‬ሻ and ݀݁݃ሺ‫ݒ‬ሻ are denoted as the degree of a vertex ‫ݑ‬ and ‫ݒ‬ respectively. The equitable domination number of a graph ߛ ሺ‫ܩ‬ሻ of ‫ܩ‬ is the minimum cardinality of an equitable dominating set of ‫.ܩ‬ An equitable dominating set ‫ܦ‬ is said to be an equitable total dominating set if the induced subgraph ‫ۄܦۃ‬ has no isolated vertices. The equitable total domination number ߛ ௧ ሺ‫ܩ‬ሻ of ‫ܩ‬ is the minimum cardinality of an equitable total dominating set of ‫.ܩ‬ In this paper, we initiate a study on new domination parameter equitable total domination number of a graph, characterization is given for equitable total dominating set is minimal and also discussed Northaus-Gaddum type results

Anaesthesia and PET of the Brain

Although drugs have been used to administer general anaesthesia for more than a century and a half, relatively little was known until recently about the molecular and cellular effects of the anaesthetic agents and the neurobiology of anaesthesia. Positron emission tomography (PET) and single-photon emission computed tomography (SPECT) studies have played a valuable role in improving this knowledge. PET studies using 11C-flumazenil binding have been used to demonstrate that the molecular action of some, but not all, of the current anaesthetic agents is mediated via the GABAA receptor. Using different tracers labelled with 18F, 11C and 15O, PET studies have shown the patterns of changes in cerebral metabolism and blood flow associated with different intravenous and volatile anaesthetic agents. Within classes of volatile agents, there are minor variations in patterns. More profound differences are found between classes of agents. Interestingly, all agents cause alterations in the blood flow and metabolism of the thalamus, providing strong support for the hypothesis that the anaesthetic agents interfere with consciousness by interfering with thalamocortical communication.</p