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.
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.
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.
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.
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.
Photocatalysis mechanism has acquired an egregious amount of consideration for a wide spectrum of utilizations in the environmental and energy fields. The potential applications which are rigorously ...associated with environmental reclamation and the latest energy developments include water splitting, pollutant decomposition, and photocatalytic diminution of CO
2
. This study deals with the discussion of the crystal structure of the polyphenylene network for photocatalysis
and the computation of some degree-based topological indices which are very beneficial for estimating the reactivity of the corresponding compounds. Particularly, we extend this computation to the analysis of the thermodynamic properties namely entropy and heat of formation which could be beneficial in the structure amendment
for effective implementation.
The founding of any television broadcaster demands substantial financial investments because the production of programmes costs the same regardless of whether one is producing a programme for ...millions or several thousand viewers. Almost all television broadcasters began their development as parts of radio stations (BBC in the United Kingdom, CBS and NBC in the USA). The television broadcaster founded by Radio Zagreb as one of its departments is no exception.The rapid development of television in the technological and programmatic sense after World War II led to it taking away an increasingly large media space from other information and entertainment sources, so that it quickly became independent and grew into the dominant mass medium. Public television in Croatia (Yugoslavia) underwent the same development path as other public television broadcasters in Europe, albeit much later than the broadcasters that served as its role models (BBC and RAI) and in significantly tougher financial and social circumstances. The enthusiasm and professionalism of the people involved in the creation of television in Zagreb were of decisive importance for its later development. All those who joined the project showed a readiness to master something completely unknown and to learn on the go.Many have written about the time and circumstances in which television appeared in Croatia as the time of enthusiasts of Radio Zagreb. As Ivan Šibl said, the enthusiasm and passion of these people for the new medium was not curbed by the eternal lack of money or by the political and social circumstances of the time. Starting from almost nothing, on their on their own initiative, with much ingenuity, professionalism, and, above all, much love, they created the first television broadcaster in Yugoslavia. Sadly, instead of affirmation, this pioneering work of Radio Zagreb caused much envy and obstructions.Still, once they had begun, they became unstoppable. They learned on the go and, learning from their mistakes, created a programme of increasingly higher quality. Even though they planned to make a television network in Croatia in only a few years (1956–1960), the financial and political circumstances did not allow this, so the whole process dragged out for almost two decades. But they managed to create the foundations of modern television from almost nothing. The increasing viewership through the years is a clear indicator of the success of their work.No less important, in the time and in social conditions in which they lived, was their courage to consciously choose to broadcast foreign television programmes, because they could not influence the contents of Italian and Austrian television. Even though these were mostly sports, entertainment, and cultural programmes, they opened a ‘window into the world’ for their audience.In a way, the beginning of television in Zagreb is linked to football. Everything always began with the broadcasting of football matches, from persuading individuals to attracting viewers at the very beginning. Of course, the sports programme was always the most viewed part of the television programme.However, once they began to produce a television programme, they became unstoppable. Thanks to numerous enthusiasts, starting from just one small, makeshift studio, they created the foundations upon which most public—and private—television broadcasters in today’s Croatia rest.
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 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.
PDF
