Unicyclic and bicyclic graphs with maximum exponential second Zagreb index

Let G = (V(G), E(G)) be a graph. The complement of G is denoted by Gc. The forgotten topological index of G, denoted F(G), is defined as the sum of the cubes of the degrees of all the vertices in G. The second Zagreb index of G, denoted M2(G), is defined as the sum of the products of the degrees of pairs of adjacent vertices in G. A graph Gisk-Hamiltonian if for all X ⊂V(G) with|X| ≤ k, the subgraph induced byV(G) - Xis Hamiltonian. Clearly, G is 0-Hamiltonian if and only if G is Hamiltonian. A graph Gisk-path-coverableifV(G) can be covered bykor fewer vertex-disjoint paths. Using F(Gc) and M2(Gc), Li obtained several sufficient conditions for Hamiltonian and traceable graphs (Rao Li, Topological Indexes and Some Hamiltonian Properties of Graphs). In this chapter, the author presents sufficient conditions based upon F(Gc) and M2(Gc)for k-Hamiltonian, k-edge-Hamiltonian, k-path-coverable, k-connected, and k-edge-connected graphs.

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Topological properties of Graphene using some novel neighborhood degree-based topological indices

International Journal of Mathematics for Industry ◽

10.1142/s2661335219500060 ◽

2019 ◽

Vol 11 (01) ◽

pp. 1950006 ◽

Cited By ~ 2

Author(s):

Sourav Mondal ◽

Nilanjan De ◽

Anita Pal

Keyword(s):

Real Number ◽

Chemical Structure ◽

Topological Index ◽

Line Graph ◽

Topological Indices ◽

Index Formula ◽

Topological Properties ◽

Zagreb Index ◽

Physiochemical Properties ◽

Second Zagreb Index

Topological indices are numeric quantities that transform chemical structure to real number. Topological indices are used in QSAR/QSPR studies to correlate the bioactivity and physiochemical properties of molecule. In this paper, some newly designed neighborhood degree-based topological indices named as neighborhood Zagreb index ([Formula: see text]), neighborhood version of Forgotten topological index ([Formula: see text]), modified neighborhood version of Forgotten topological index ([Formula: see text]), neighborhood version of second Zagreb index ([Formula: see text]) and neighborhood version of hyper Zagreb index ([Formula: see text]) are obtained for Graphene and line graph of Graphene using subdivision idea. In addition, these indices are compared graphically with respect to their response for Graphene and line graph of subdivision of Graphene.

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On Some New Neighborhood Degree-Based Indices for Some Oxide and Silicate Networks

J ◽

10.3390/j2030026 ◽

2019 ◽

Vol 2 (3) ◽

pp. 384-409

Author(s):

Sourav Mondal ◽

Nilanjan De ◽

Anita Pal

Keyword(s):

Molecular Structure ◽

Network Theory ◽

Topological Index ◽

Applied Mathematics ◽

Reaction Network ◽

Topological Indices ◽

Zagreb Index ◽

Second Zagreb Index ◽

Real World Problems ◽

Chemical Reaction Network Theory

Topological indices are numeric quantities that describes the topology of molecular structure in mathematical chemistry. An important area of applied mathematics is the chemical reaction network theory. Real-world problems can be modeled using this theory. Due to its worldwide applications, chemical networks have attracted researchers since their foundation. In this report, some silicate and oxide networks are studied, and exact expressions of some newly-developed neighborhood degree-based topological indices named as the neighborhood Zagreb index ( M N ), the neighborhood version of the forgotten topological index ( F N ), the modified neighborhood version of the forgotten topological index ( F N ∗ ), the neighborhood version of the second Zagreb index ( M 2 ∗ ), and neighborhood version of the hyper Zagreb index ( H M N ) are obtained for the aforementioned networks. In addition, a comparison among all the indices is shown graphically.

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On the reduced second Zagreb index of graphs

Rocky Mountain Journal of Mathematics ◽

10.1216/rmj.2020.50.975 ◽

2020 ◽

Vol 50 (3) ◽

pp. 975-988 ◽

Cited By ~ 1

Author(s):

Fang Gao ◽

Kexiang Xu

Keyword(s):

Zagreb Index ◽

Second Zagreb Index

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Topological indices of non-commuting graph of dihedral groups

Malaysian Journal of Fundamental and Applied Sciences ◽

10.11113/mjfas.v14n0.1270 ◽

2018 ◽

Vol 14 ◽

pp. 473-476 ◽

Cited By ~ 2

Author(s):

Nur Idayu Alimon ◽

Nor Haniza Sarmin ◽

Ahmad Erfanian

Keyword(s):

Wiener Index ◽

Topological Indices ◽

First Zagreb Index ◽

Dihedral Groups ◽

Zagreb Index ◽

Second Zagreb Index ◽

Commuting Graph ◽

Vertex Set ◽

Group A ◽

Group Of Symmetries

Assume is a non-abelian group A dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. The non-commuting graph of denoted by is the graph of vertex set whose vertices are non-central elements, in which is the center of and two distinct vertices and are joined by an edge if and only if In this paper, some topological indices of the non-commuting graph, of the dihedral groups, are presented. In order to determine the Edge-Wiener index, First Zagreb index and Second Zagreb index of the non-commuting graph, of the dihedral groups, previous results of some of the topological indices of non-commuting graph of finite group are used. Then, the non-commuting graphs of dihedral groups of different orders are found. Finally, the generalisation of Edge-Wiener index, First Zagreb index and Second Zagreb index of the non-commuting graphs of dihedral groups are determined.

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On Leap Reduced Reciprocal Randic and Leap Reduced Second Zagreb Indices of Some Graphs

Scientific Inquiry and Review ◽

10.32350/sir.32.04 ◽

2019 ◽

Vol 3 (2) ◽

pp. 27-35

Author(s):

Fazal Dayan ◽

Muhammad Javaid ◽

Muhammad Aziz ur Rehman

Keyword(s):

Topological Indices ◽

Randić Index ◽

Zagreb Index ◽

Randic Index ◽

Zagreb Indices ◽

Second Zagreb Index ◽

Second Degree

Naji et al. introduced the leap Zagreb indices of a graph in 2017 which are new distance-degree-based topological indices conceived depending on the second degree of vertices. In this paper, we have defined the first and second leap reduced reciprocal Randic index and leap reduced second Zagreb index for selected wheel related graphs.

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On the Inverse Problem for Some Topological Indices

Journal of Mathematics ◽

10.1155/2021/9411696 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Durbar Maji ◽

Ganesh Ghorai ◽

Muhammad Khalid Mahmood ◽

Md. Ashraful Alam

Keyword(s):

Inverse Problem ◽

Topological Indices ◽

Negative Integer ◽

First Zagreb Index ◽

Zagreb Index ◽

Molecular Tree ◽

Bicyclic Graphs

The study of the inverse problem (IP) based on the topological indices (TIs) deals with the numerical relations to TIs. Mathematically, the IP can be expressed as follows: given a graph parameter/TI that assigns a non-negative integer value g to every graph within a given family G of graphs, find some G ∈ G for which TI G = g . It was initiated by the Zefirov group in Moscow and later Gutman et al. proposed it. In this paper, we have established the IP only for the Y -index, Gourava indices, second hyper-Zagreb index, reformulated first Zagreb index, and reformulated F -index since they are closely related to each other. We have also studied the same which is true for the molecular, tree, unicyclic, and bicyclic graphs.

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Hyper Zagreb indices of composite graphs

International Journal of Advanced Mathematical Sciences ◽

10.14419/ijams.v6i1.8406 ◽

2016 ◽

Vol 4 (2) ◽

pp. 47 ◽

Cited By ~ 1

Author(s):

Sharmila Devi ◽

V. Kaladevi

Keyword(s):

Molecular Graph ◽

Sum Of Squares ◽

First Zagreb Index ◽

Zagreb Index ◽

Zagreb Indices ◽

Second Zagreb Index ◽

The First Zagreb Index ◽

Thorn Graph

For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the degrees of vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Similarly, the hyper Zagreb index is defined as the sum of square of degree of vertices over all the edges. In this paper, First we obtain the hyper Zagreb indices of some derived graphs and the generalized transformations graphs. Finally, the hyper Zagreb indices of double, extended double, thorn graph, subdivision vertex corona of graphs, Splice and link graphs are obtained.

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