Sum Labeling for Some Star and Cycle Related Special Graphs

A sum labeling is a mapping from the vertices of G into the positive integers such that, for any two vertices u, v V (G) with labels (u) and (v), respectively, (uv) is an edge iff (u) + (v) is the label of another vertex in V (G). Any graph supporting such a labeling is called a sum graph. It is necessary to add (as a disjoint union) a component to sum label a graph. This disconnected component is a set of isolated vertices known as isolates and the labeling scheme that requires the fewest isolates is termed optimal. The number of isolates required for a graph to support a sum labeling is known as the sum number of the graph. In this paper, we will obtain optimal sum labeling scheme for some star and cycle related special graphs

Antibacterial activity of ovary extract from sea urchin Diadema setosum

Objective: Sea urchin gonad is considered as a highly prized delicacy in several countries. It is also rich in valuable bioactive compounds including polyunsaturated fatty acids (PUFAs) and β-carotene. This study was undertaken to examine the antimicrobial properties of the ovary extract from sea urchin Diadema setosum against selected Gram-negative and Gram-positive bacteria. Materials and methods: The ovary extract was obtained using two different solvents such as methanol and chloroform. The obtained extract was used to examine its potential antimicrobial properties against the following 11 bacterial species using the disc diffusion method: Gram-negative bacteria (Salmonella typhi, Salmonella typhimurium, Shigella flexneri, Pseudomonas aeruginosa, Aeromonas hydrophila, Acinetobacter sp, Citrobacter freundii and Klebsiella pneumonia) and Gram-positive bacteria (Bacillus subtilis, Staphylococcus epidermidis and Staphylococcus aureus). The activity was measured in terms of zone of inhibition (mm). Results: The methanol extract exhibited a higher zone of inhibition against all the bacteria taken for examination. Whereas, the ovary extract obtained by chloroform did not show any antimicrobial activity against S. typhi, S. epidermidis, C. freundii and K. pneumonia. The results indicated that the ovary extract obtained by methanol extracts are capable of inhibiting the growth of pathogenic microbes taken for analysis. Moreover, the result indicates the presence of antimicrobial agents in sea urchin ovary. Conclusions: The study suggests that the ovary extract of D. setosum may be a potential source of antimicrobial agent for pathogenic microorganisms

Szegedski topološki indeksi in učinkovitost prerezne metode: primer melemskih struktur

The Szeged index is a bond-additive topological descriptor that quantifies each bond\u27s terminal atoms based on their closeness sets which is measured by multiplying the number of atoms in the closeness sets. Based on the high correlation between the Szeged index and the physico-chemical properties of chemical compounds, Szeged-like indices have been proposed by considering closeness sets with bond counts and other mathematical operations like addition and subtraction. As there are many ways to compute the Szeged-like indices, the cut method is predominantly used due to its complexity compared to other approaches based on algorithms and interpolations. Yet, we here analyze the usefulness of the cut method in the case of melem structures and find that it is less effective when the size and shape of the cavities change in the structures.Szegedski indeks je topološki deskriptor, ki kvantificira končne atome vsake vezi na podlagi njihovih množic bližine, ki se merijo s številom atomov v množicah bližine. Na podlagi visoke korelacije med szegedskim indeksom in fizikalno-kemijskimi lastnostmi kemičnih spojin so bili predlagani podobni indeksi in sicer z upoštevanjem množic bližine, štetjem vezi ter drugimi matematičnimi operacijami, kot sta seštevanje in odštevanje. Ker obstaja veliko načinov za izračun szegedskih indeksov, se prerezna metoda pretežno uporablja zaradi svoje kompleksnosti v primerjavi z drugimi pristopi, ki temeljijo na algoritmih in interpolacijah. Tukaj analiziramo uporabnost prerezne metode v primeru melemskih struktur in ugotavljamo, da je manj učinkovita, če se v strukturah spremenita velikost in oblika votlin

BALANCED HESITANCY FUZZY GRAPHS

In this paper, a new Hesitancy Fuzzy Graph Model called Balanced Hesitancy Fuzzy Graphs (BHFGs) is introduced. Also, we discuss the various concepts related with Balanced Hesitancy Fuzzy Graphs with their graphical representations. Further we develop the concept of self complementary hesitancy fuzzy graphs along with the theoretical illustration