Roslan Hasni

On Topological Indices of Certain Families of Nanostar Dendrimers

A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR)/quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Randić connectivity index, atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are used to predict the bioactivity of different chemical compounds. A dendrimer is an artificially manufactured or synthesized molecule built up from the branched units called monomers. In this paper, the fourth version of ABC index and the fifth version of GA index of certain families of nanostar dendrimers are investigated. We derive the analytical closed formulas for these families of nanostar dendrimers. The obtained results can be of use in molecular data mining, particularly in researching the uniqueness of tested (hyper-branched) molecular graphs.

Algebraic Integers as Chromatic and Domination Roots

Let be a simple graph of order and . A mapping is called a -colouring of if whenever the vertices and are adjacent in . The number of distinct -colourings of , denoted by , is called the chromatic polynomial of . The domination polynomial of is the polynomial , where is the number of dominating sets of of size . Every root of and is called the chromatic root and the domination root of , respectively. Since chromatic polynomial and domination polynomial are monic polynomial with integer coefficients, its zeros are algebraic integers. This naturally raises the question: which algebraic integers can occur as zeros of chromatic and domination polynomials? In this paper, we state some properties of this kind of algebraic integers.

Chromaticity of a family of 5-partite graphs

Abstract Let P(G,λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G ∼ H, if P(G,λ) = P(H,λ). We write [G] = {H∣H ∼ G}. If [G] = {G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 5-partite graphs G with 5n vertices according to the number of 6-independent partitions of G. Using these results, we investigate the chromaticity of G with certain stars or matching deleted parts . As a by-product, two new families of chromatically unique complete 5-partite graphs G with certain stars or matching deleted parts are obtained.

Chromatically unique 6-bridge graph theta(a,a,a,b,b,c)

For a graph

More results on computation of topological indices of certain networks

G

3-total edge product cordial labeling of graphs

, let

Atom-bond connectivity index of graph with three edges added

P(G,\lambda)

Fourth order connectivity index of polyphenylene dendrimers

denote the chromatic polynomial of

3-TOTAL EDGE PRODUCT CORDIAL LABELING OF GRAPHS

G

On the Atom-Bond Connectivity Index of Some Families of Dendrimers

. Two graphs