Topological indices are numbers related to sub-atomic graphs to allow quantitative structure-movement/property/danger connections. These topological indices correspond to some specific ...physico-concoction properties such as breaking point, security, strain vitality of chemical compounds. The idea of topological indices were set up in compound graph hypothesis in view of vertex degrees. These indices are valuable in the investigation of mitigating exercises of specific Nanotubes and compound systems. In this paper, we discuss Zagreb types of indices and Zagreb polynomials for a few Nanotubes covered by cycles.
First (M1) and second (M2) Zagreb indices are graph invariants that originate from chemical researches on total π-electron energy of conjugated molecules. There is a legion of articles dealing with ...these two indices. This paper presents upper bounds on Zagreb indices of trees in terms of domination number. These are strict bounds, and extremal trees are characterized. In addition, a lower bound for the first Zagreb index of trees with a given domination number is determined and the extremal trees are characterized as well. Finally, using previously known upper bound for Harary index (H) in terms of M1 and M2, a unique tree with given domination number that maximizes H is characterized.
Dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core (Ashrafi and Mirzargar, 2008 3; Chen et al., 2014 7; Klajnert ...and Bryszewska, 2001 26; Yamamoto et al., 2002 36). These are key molecules in nanotechnology and can be put to good use. Topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity/property/toxicity relationships. These topological indices correlate certain physico-chemical properties like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index and Zagreb polynomials for some nanostar dendrimers.
On difference of Zagreb indices Furtula, Boris; Gutman, Ivan; Ediz, Süleyman
Discrete Applied Mathematics,
12/2014, Letnik:
178
Journal Article
Recenzirano
Odprti dostop
The classical first and second Zagreb indices of a graph G are defined as M1=∑vdv2 and M2=∑uvdudv, where dv is the degree of the vertex v of G. So far, the difference of M1 and M2 has not been ...studied. We show that this difference is closely related to the vertex-degree-based invariant RM2=∑uv(du−1)(dv−1), and determine a few basic properties of RM2.
Graph theory is used for modeling, designing, analysis and understanding chemical structures or chemical networks and their properties. The molecular graph is a graph consisting of atoms called ...vertices and the chemical bond between atoms called edges. In this article, we study the chemical graphs of carbon graphite and crystal structure of cubic carbon. Moreover, we compute and give closed formulas of degree based additive topological indices, namely hyper-Zagreb index, first multiple and second multiple Zagreb indices, and first and second Zagreb polynomials.
A forgotten topological index Furtula, Boris; Gutman, Ivan
Journal of mathematical chemistry,
04/2015, Letnik:
53, Številka:
4
Journal Article
Recenzirano
In 1972, within a study of the structure-dependency of total
π
-electron energy (
E
), it was shown that
E
depends on the sum of squares of the vertex degrees of the molecular graph (later named ...first Zagreb index), and thus provides a measure of the branching of the carbon-atom skeleton. In the same paper, also the sum of cubes of degrees of vertices of the molecular graph was shown to influence
E
, but this topological index was never again investigated and was left to oblivion. We now establish a few basic properties of this “forgotten topological index” and show that it can significantly enhance the physico-chemical applicability of the first Zagreb index.
The Zagreb indices (ZIs) are important graph invariants that are used extensively in many different fields in mathematics and chemistry, such as network theory, spectral graph theory, fuzzy graph ...theory (FGT) and molecular chemistry, etc. The hyper-ZI is introduced especially for fuzzy graphs (FGs) in this study. The study computes this index's bounds for a variety of FG types, including paths, cycles, stars, complete FGs and partial fuzzy subgraphs. It is shown that isomorphic FGs produce the same values for this index. Moreover, interesting connections are established between the hyper-ZI and the second ZI for FGs. Moreover, bounds on this index are found for the following operations: direct product, Cartesian product, composition, join, union, strong product and semi-strong product of two FGs. In the end, the effectiveness of this index is compared with three other topological indices: hyper-ZI for crisp graphs, first ZI for FGs and F-index for FGs, in an analysis of the crime “Murder” in India. While the hyper-ZI for FGs, first ZI for FGs and F-index for FGs yield similar outcomes, the hyper-ZI for FGs demonstrates superior realism in detecting crimes in India compared to its crisp graph counterpart.
The first and second Zagreb indices, since its inception have been subjected to an extensive research in the physio- chemical analysis of compounds. In 6 Hanyuan Deng et.al computed the first ...and second Zagreb indices of four new operations on a graph defined by M. Eliasi, B. Taeri in 4. Motivated from this we define a new operation on graphs and compute the first and second Zagreb indices of the resultant graph. We illustrate the results with some examples.
Inverse problem for Zagreb indices Yurtas, Aysun; Togan, Muge; Lokesha, Veerebradiah ...
Journal of mathematical chemistry,
15/2, Letnik:
57, Številka:
2
Journal Article
Recenzirano
The inverse problem for integer-valued topological indices is about the existence of a graph having its index value equal to a given integer. We solve this problem for the first and second Zagreb ...indices, and present analogous results also for the forgotten and hyper-Zagreb index. The first Zagreb index of connected graphs can take any even positive integer value, except 4 and 8. The same is true if one restricts to trees or to molecular graphs. The second Zagreb index of connected graphs can take any positive integer value, except 2, 3, 5, 6, 7, 10, 11, 13, 15 and 17. The same is true if one restricts to trees or to molecular graphs.
Let G be a graph with n vertices and d
i is the degree of its ith vertex (d
i is the degree of v
i). In this article, we compute the redefined first Zagreb index, redefined second Zagreb index, ...redefined third Zagreb index, augmented Zagreb index of graphs carbon nanocones CNC
kn, and nanotori C4C6C8(p,q). Also, compute the multiplicative redefined first Zagreb index, multiplicative redefined second Zagreb index, multiplicative redefined third Zagreb index, multiplicative augmented Zagreb index of carbon nanocones CNC
kn, and nanotori C4C6C8(p,q).
The molecular graph of nanocones have conical structures with a cycle of length k at its core and n layers of hexagons placed at the conical surface around its center, show carbon nanocones in this figure.
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