By $d(v|G)$ and $d_2(v|G)$ are denoted the number of first and second neighbors of the vertex $v$ of the graph $G$. The first, second, and third leap Zagreb indices of $G$ are defined as ...$LM_1(G) = \sum_{v \in V(G)} d_2(v|G)^2$, $LM_2(G) = \sum_{uv \in E(G)} d_2(u|G)\,d_2(v|G)$, and $LM_3(G) = \sum_{v \in V(G)} d(v|G)\,d_2(v|G)$, respectively. In this paper, we generalize the results of Naji et al. Commun. Combin. Optim. {\bf 2} (2017), 99--117, pertaining to trees and unicyclic graphs. In addition, we determine upper and lower bounds on these leap Zagreb indices and characterize the extremal graphs.
Topological indices are useful in QSAR/QSPR studies for modeling biological and physiochemical properties of molecules. The neighborhood Zagreb index (M N ) is a novel topological index having good ...correlations with some physiochemical properties. For a simple connected graph G, the neighborhood Zagreb index is the totality of square of δ G (v) over the vertex set, where δ G (v) is the total count of degrees of all neighbors of v in G. In this report, some bounds are established for the neighborhood Zagreb index. Some explicit expressions of the index for some graph operations are also computed, which are used to obtain the index for some chemically significant molecular graphs.
For a connected graph G, the second Zagreb eccentricity index of G is defined as ξ2(G)=∑uv∈E(G)eG(u)eG(v), where eG(u) denotes the eccentricity of u in G. In this paper, we give a graft ...transformation to increase the second Zagreb eccentricity indices of graphs, and as applications, we determine n-vertex bicyclic graphs with maximum and second maximum second Zagreb eccentricity indices, respectively.
In this paper we compute the correct values of Zagreb indices and the forgotten index of two classes of composite graphs “disjunction and symmetric difference”. In this way we correct some previously ...reported formulas given in https://doi.org/10.1016/j.dam.2008.06.015, https://doi.org/10.1016/j.dam.2010.05.017 and https://link.springer.com/article/10.1186/s40064-016-1864-7. As a consequence, we compute the correct values of the respective.
•Give and prove the correct formulas of Zagreb indices and their coindices of symmetric difference.•Give and prove the correct formulas of Zagreb indices and their coindices of disjunction.•Give and prove the correct formulas of F-coindex of symmetric difference.
Topological indices collect information from the graph of molecule and help to predict properties of the underlying molecule. Zagreb indices are among the most studied topological indices due to ...their applications in chemistry. In this paper, we compute first and second reverse Zagreb indices, reverse hyper-Zagreb indices and their polynomials of Prophyrin, Propyl ether imine, Zinc Porphyrin and Poly (ethylene amido amine) dendrimers.
On New Variance of Zagreb Indices Reddy, D T Hanumantha; Rao, M V Chakradhara
IAENG international journal of applied mathematics,
02/2024, Letnik:
54, Številka:
2
Journal Article
Recenzirano
Odprti dostop
In QSPR studies topological indices plays vital role. To enrich this field we put forward novel topological indices namely Mass Zagreb indices. In this paper first we study the mathematical ...properties of new variance of Zagreb indices then followed by its chemical applications in QSPR studies.
The first Zagreb index M1 of a graph is defined as the sum of the square of every vertex degree, and the second Zagreb index M2 of a graph is defined as the sum of the product of vertex degrees of ...each pair of adjacent vertices. In Furtula et al. (2014) Furtula, Gutman and Ediz first proposed the reduced second Zagreb index as RM2(G)=∑uv∈E(G)(d(u)−1)(d(v)−1)=ΔM(G)+m(G),where ΔM(G) is the difference between M2 and M1 of graph G and m(G) is the size of G. In this paper, some graph transformations are introduced. We study the monotonicity of RM2(G) with respect to these graph transformations. Then based on these properties, we present sharp upper and lower bounds on RM2(G) of connected n-vertex cyclic graphs with given number of cut vertices. All the corresponding extremal graphs are identified.
In the period between the two world wars, Zagreb did not have a general regulatory basis according to which it would develop. Partial regulatory bases are created for individual areas. The western ...part of the city, which is bounded by the Republic of Austria Street in the east, Ilica in the north, the railway line in the south and the Črnomerca stream in the west, and which was included in the Regulatory basis from 1887 as an extension of the Lower Town, is being built by interpolating the blocks according to several regulatory bases created for individual regions. Industrial complexes, which at that time had priority over military ones, did not leave a significant urban element in the urban sense, and exceptions are rare, such as the administration building of the Factory "Hinka Francka sinovi d.d.". The construction in the western part of Zagreb between the two world wars was of a lower design and, in terms of construction, of lower quality than the previous era.
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