General reduced second Zagreb index of graph operations

Khoeilar, R.; Jahanbani, Akbar

doi:10.1142/s1793557121500820

Cited by 2 publications

(1 citation statement)

References 9 publications

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“…For the corona product (COP) [27] of J 1 and J 2 , denoted by J 1 ∘ J 2 , the degree of a vertex r ∈ J 1 ∘ J 2 is given in Table 3. Now, we obtain the explicit expression of RSZI for corona product of two graphs.…”

Section: Corona Productmentioning

confidence: 99%

On the Reformulated Second Zagreb Index of Graph Operations

Maji

Ghorai

Gaba

2021

Journal of Chemistry

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Topological indices (TIs) are expressed by constant real numbers that reveal the structure of the graphs in QSAR/QSPR investigation. The reformulated second Zagreb index (RSZI) is such a novel TI having good correlations with various physical attributes, chemical reactivities, or biological activities/properties. The RSZI is defined as the sum of products of edge degrees of the adjacent edges, where the edge degree of an edge is taken to be the sum of vertex degrees of two end vertices of that edge with minus 2. In this study, the behaviour of RSZI under graph operations containing Cartesian product, join, composition, and corona product of two graphs has been established. We have also applied these results to compute RSZI for some important classes of molecular graphs and nanostructures.

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Section: Corona Productmentioning

confidence: 99%

On the Reformulated Second Zagreb Index of Graph Operations

Maji

Ghorai

Gaba

2021

Journal of Chemistry

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On General Reduced Second Zagreb Index of Graphs

2022

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Graph-based molecular structure descriptors (often called “topological indices”) are useful for modeling the physical and chemical properties of molecules, designing pharmacologically active compounds, detecting environmentally hazardous substances, etc. The graph invariant GRMα, known under the name general reduced second Zagreb index, is defined as GRMα(Γ)=∑uv∈E(Γ)(dΓ(u)+α)(dΓ(v)+α), where dΓ(v) is the degree of the vertex v of the graph Γ and α is any real number. In this paper, among all trees of order n, and all unicyclic graphs of order n with girth g, we characterize the extremal graphs with respect to GRMα(α≥−12). Using the extremal unicyclic graphs, we obtain a lower bound on GRMα(Γ) of graphs in terms of order n with k cut edges, and completely determine the corresponding extremal graphs. Moreover, we obtain several upper bounds on GRMα of different classes of graphs in terms of order n, size m, independence number γ, chromatic number k, etc. In particular, we present an upper bound on GRMα of connected triangle-free graph of order n>2, m>0 edges with α>−1.5, and characterize the extremal graphs. Finally, we prove that the Turán graph Tn(k) gives the maximum GRMα(α≥−1) among all graphs of order n with chromatic number k.

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General reduced second Zagreb index of graph operations

Cited by 2 publications

References 9 publications

On the Reformulated Second Zagreb Index of Graph Operations

On the Reformulated Second Zagreb Index of Graph Operations

On General Reduced Second Zagreb Index of Graphs

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