Edge restricted detour index of some graphs

Abdullah, Hewa Y.; Omar, Zhian I.

doi:10.1080/09720529.2019.1624062

Cited by 3 publications

(3 citation statements)

References 3 publications

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“…Kaladevi and Abinayaa [37] studied spectral properties of the detour index in relation with the Laplacian energy of graphs. Recently, Abdullah and Omar [38] introduced the restricted edge version of the detour index and studied it for some families of graphs. Tang et al [39] studied Zagreb connection indices of some operation of graphs.…”

Section: E(g) ⊆mentioning

confidence: 99%

On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes

Hayat

Malik

Ahmad

et al. 2021

Mathematical Problems in Engineering

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A convex polytope is the convex hull of a finite set of points in the Euclidean space ℝ n . By preserving the adjacency-incidence relation between vertices of a polytope, its structural graph is constructed. A graph is called Hamilton-connected if there exists at least one Hamiltonian path between any of its two vertices. The detour index is defined to be the sum of the lengths of longest distances, i.e., detours between vertices in a graph. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering, whereas the detour index has important applications in chemistry. Checking whether a graph is Hamilton-connected and computing the detour index of an arbitrary graph are both NP-complete problems. In this paper, we study these problems simultaneously for certain families of convex polytopes. We construct two infinite families of Hamilton-connected convex polytopes. Hamilton-connectivity is shown by constructing Hamiltonian paths between any pair of vertices. We then use the Hamilton-connectivity to compute the detour index of these families. A family of non-Hamilton-connected convex polytopes has also been constructed to show that not all convex polytope families are Hamilton-connected.

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Section: E(g) ⊆mentioning

confidence: 99%

On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes

Hayat

Malik

Ahmad

et al. 2021

Mathematical Problems in Engineering

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“…The detour index has important applications in chemistry. Applications of this parameter in quantitative structure activity and property relationship models were put forward in (2,3) . In (4) a comparative analysis with the Wiener index in terms of applicability in correlating structure boiling point of organic compounds.…”

Section: Introductionmentioning

confidence: 99%

Modified Detour Index of Hamiltonian Connected (Laceable) Graphs

Nagarathnamma,

Shenoy,

Krishna

2024

IJST

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Objectives: To explore the bounds for the modified detour index of certain Hamiltonian connected and laceable graphs. Methods: The Wiener index , detour index and the modified detour index are used. Findings: Here we introduce the modified detour index and its least upper bounds for Hamiltonian connected and laceable graphs, by formulating the constraints. Novelty: Based on the modified detour index, the bounds for some special graphs such as: Hamiltonian connected graphs of two families of convex polytopes ( and ) and Hamiltonian laceable graphs of spider graph ( ) and image graph of prism graph ( ) are encountered here. Keywords: Hamiltonian graph, Hamiltonian connected, Hamiltonian laceable, Wiener index, detour index

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“…Kaladevi [54] studied spectral properties of the detour index in relation with the Laplacian energy of graphs. Recently, Abdullah and Omar [55] introduced the restricted edge version of the detour index and studied it for some families of graphs.…”

Section: Introductionmentioning

confidence: 99%

Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index

Hayat

Khan

et al. 2021

Complexity

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A connected graph is called Hamilton-connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton-connected is an NP-complete problem. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for a graph is also an NP-complete problem. In this paper, we study the Hamilton-connectivity of convex polytopes. We construct three infinite families of convex polytopes and show that they are Hamilton-connected. An infinite family of non-Hamilton-connected convex polytopes is also constructed, which, in turn, shows that not all convex polytopes are Hamilton-connected. By using Hamilton connectivity of these families of graphs, we compute exact analytical formulas of their detour index.

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Edge restricted detour index of some graphs

Cited by 3 publications

References 3 publications

On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes

On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes

Modified Detour Index of Hamiltonian Connected (Laceable) Graphs

Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index

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