Computation of Wiener Index, Reciprocal Wiener Index and Peripheral Wiener Index Using Adjacency Matrix

Rajendra, R.; Reddy, P. Siva Kota; Prabhavathi, M.

doi:10.56827/seajmms.2022.1803.23

Cited by 2 publications

(1 citation statement)

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“…The Wiener index W (G) of a connected graph G is defined to be the sum of distances between all vertex pairs in G. The Wiener index is substantially used in theoretical chemistry for the design of quantitative structure-property relations (mainly with physico-chemical properties) and quantitative structure-activity relations including biological activities of the respective chemical compounds. For new topological indices, we suggest the reader to refer the papers [7], [9][10][11][12]. Rajendra et al [13] have recently introduced the concept of peripheral geodesic index.…”

Section: Introductionmentioning

confidence: 99%

Chelo Index for Graphs

Rajendra¹,

Reddy²,

Harshavardhana³

et al. 2023

SEAJMMS

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It is exciting to study and establish relationships between the physical properties and the molecular structure of chemicals and there is a scope for defining new topological indices. This paper aims to introduce a new topological index for graphs called Chelo index. The Chelo index of a graph G is the sum of five times order of G and two times the number of geodesics of length 3 minus the number of geodesics between peripheral vertices. We compute Chelo index for some standard graphs and observe the correlation between some physical properties and Chelo index for low alkanes. Also, we establish a formulae for computing the number of 176 graph geodesics in a graph and the Chelo index using the adjacency matrix

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Section: Introductionmentioning

confidence: 99%

Chelo Index for Graphs

Rajendra¹,

Reddy²,

Harshavardhana³

et al. 2023

SEAJMMS

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Stress-difference index for graphs

Rajendra,

Reddy,

Harshavardhana

2024

B Soc Paran Mat

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The stress of a vertex is a node centrality index, which has been introduced by Shimbel (1953). The stress of a vertex in a graph is the number of geodesics (shortest paths) passing through it. A topological index of a chemical structure (graph) is a number that correlates the chemical structure with chemical reactivity or physical properties. In this paper, we introduce a new topological index for graphs called stress-difference index using stresses of vertices. Further, we establish some inequalities, prove some results and compute stress-difference index for some standard graphs. Also, we found that there is a positive correlation between the stress-difference index and some physical properties of lower alkanes.

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Computation of Wiener Index, Reciprocal Wiener Index and Peripheral Wiener Index Using Adjacency Matrix

Abstract: In this short paper, we establish formulae to compute Wiener index, reciprocal Wiener index and peripheral Wiener index of graphs using adjacency matrix. Further, we present algorithms for the same

Cited by 2 publications

References 5 publications

Chelo Index for Graphs

Chelo Index for Graphs

Stress-difference index for graphs

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