On the Inverse Problem for Some Topological Indices

Maji, Durbar; Ghorai, Ganesh; Mahmood, Muhammad Khalid; Alam, Md. Ashraful

doi:10.1155/2021/9411696

Cited by 11 publications

(5 citation statements)

References 24 publications

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“…Assume T 1 = v 1 v 2 v 3 shares a single side by T 1 , it is a side v 2 v 3 , then one of the other two sides is not shared by T 3 , say the side v 1 v 2 , and the quadrilaterals v 1 v 2 v 4 v 5 unable to include v 3 , thus repeatedly we were able to crumple the triangle v 1 v 2 v 0 by v 0 within T 2 , producing unique triangles through pairwise confinement introducing the new vertex v 1 � v 2 , except the triangle T 3 , so conserving the property that no triangle consumes three children. While T 2 and T 3 share aside v 1 v 3 , then every quadrilateral v 1 v 2 v 4 v 5 that includes v 3 v 3 also includes T 3 [16]. As a result, crumpling v 1 v 2 v 0 with v 0 inside T 2 provides two families of triangles through pairwise confinements concerning v 1 � v 2 , one including v 3 and the another includingv 3 , conserving the property that three children are not taken by triangles.…”

Section: We Now Prove the Main Results Ofmentioning

confidence: 99%

Graph Theory Algorithms of Hamiltonian Cycle from Quasi‐Spanning Tree and Domination Based on Vizing Conjecture

Anuradha

Surekha

Nuthakki

et al. 2022

Journal of Mathematics

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In this study, from a tree with a quasi-spanning face, the algorithm will route Hamiltonian cycles. Goodey pioneered the idea of holding facing 4 to 6 sides of a graph concurrently. Similarly, in the three connected cubic planar graphs with two-colored faces, the vertex is incident to one blue and two red faces. As a result, all red-colored faces must gain 4 to 6 sides, while all obscure-colored faces must consume 3 to 5 sides. The proposed routing approach reduces the constriction of all vertex colors and the suitable quasi-spanning tree of faces. The presented algorithm demonstrates that the spanning tree parity will determine the arbitrary face based on an even degree. As a result, when the Lemmas 1 and 2 theorems are compared, the greedy routing method of Hamiltonian cycle faces generates valuable output from a quasi-spanning tree. In graph idea, a dominating set for a graph S = V , E is a subset D of V . The range of vertices in the smallest dominating set for S is the domination number ( S ). Vizing’s conjecture from 1968 proves that the Cartesian fabricated from graphs domination variety is at least as big as their domination numbers production. Proceeding this work, the Vizing’s conjecture states that for each pair of graphs S , L .

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Section: We Now Prove the Main Results Ofmentioning

confidence: 99%

Graph Theory Algorithms of Hamiltonian Cycle from Quasi‐Spanning Tree and Domination Based on Vizing Conjecture

Anuradha

Surekha

Nuthakki

et al. 2022

Journal of Mathematics

Self Cite

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show abstract

“…Given an oriented graph D, we can partition V(D) into V 1 and V 2 by placing each vertex v ∈ V(D) into V 1 if there exists a directed path of length k between v and a fixed vertex u, and placing into V 2 otherwise. Also, the thought can be applied to solving the indexes of graphs [22][23][24][25][26][27][28].…”

Section: Advantages and Limitationsmentioning

confidence: 99%

Seymour’s Second Neighborhood Conjecture for m-Free Oriented Graphs

2022

Mathematical Problems in Engineering

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Let D = V , E be an oriented graph with minimum out-degree δ + . For x ∈ V D , let d D + x and d D + + x be the out-degree and second out-degree of x in D , respectively. For a directed graph D , we say that a vertex x ∈ V D is a Seymour vertex if d D + + x ≥ d D + x . Seymour in 1990 conjectured that each oriented graph has a Seymour vertex. A directed graph D is called m -free if there are no directed cycles with length at most m in D . A directed graph D = V , E is called k -transitive if, for any directed x y -path of length k , there exists x , y ∈ E . In this paper, we show that (1) each δ + − 2 -free oriented graph has a Seymour vertex and (2) each vertex with minimum out-degree in m -free and 2 m + 2 -transitive oriented graph is a Seymour vertex. The latter result improves a theorem of Daamouch (2021).

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“…Some of the chemical application of the sombor index was obtained in [ 26 ]. In [ 27 ], Khalid Mahmood worked on the inverse problem for some topological indices.…”

Section: Introductionmentioning

confidence: 99%

Computational Studies on Diverse Characterizations of Molecular Descriptors for Graphyne Nanoribbon Structures

Raza,

Mahmood,

Imran

et al. 2023

Molecules

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Materials made of graphyne, graphyne oxide, and graphyne quantum dots have drawn a lot of interest due to their potential uses in medicinal nanotechnology. Their remarkable physical, chemical, and mechanical qualities, which make them very desirable for a variety of prospective purposes in this area, are mostly to blame for this. In the subject of mathematical chemistry, molecular topology deals with the algebraic characterization of molecules. Molecular descriptors can examine a compound’s properties and describe its molecular topology. By evaluating these indices, researchers can predict a molecule’s behavior including its reactivity, solubility, and toxicity. Amidst the captivating realm of carbon allotropes, γ-graphyne has emerged as a mesmerizing tool, with exquisite attention due to its extraordinary electronic, optical, and mechanical attributes. Research into its possible applications across numerous scientific and technological fields has increased due to this motivated attention. The exploration of molecular descriptors for characterizing γ-graphyne is very attractive. As a result, it is crucial to investigate and predict γ-graphyne’s molecular topology in order to comprehend its physicochemical characteristics fully. In this regard, various characterizations of γ-graphyne and zigzag γ-graphyne nanoribbons, by computing and comparing distance-degree-based topological indices, leap Zagreb indices, hyper leap Zagreb indices, leap gourava indices, and hyper leap gourava indices, are investigated.

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On the Inverse Problem for Some Topological Indices

Cited by 11 publications

References 24 publications

Graph Theory Algorithms of Hamiltonian Cycle from Quasi‐Spanning Tree and Domination Based on Vizing Conjecture

Graph Theory Algorithms of Hamiltonian Cycle from Quasi‐Spanning Tree and Domination Based on Vizing Conjecture

Seymour’s Second Neighborhood Conjecture for m-Free Oriented Graphs

Computational Studies on Diverse Characterizations of Molecular Descriptors for Graphyne Nanoribbon Structures

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