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TOSHA INDEX FOR GRAPHS

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초록

A topological index of a chemical structure (graph) is a number that correlates the chemical structure with chemical reactivity or physical properties. There are several topological indices have been defi ned on graphs using degrees of vertices/edges, for instance fi rst and second Zagreb indices. In this paper, we introduce a new topological index for graphs called Tosha index using tension on edges. Further, we establish some inequalities and compute Tosha index for some standard graphs.

Abstract

A topological index of a chemical structure (graph) is a number that correlates the chemical structure with chemical reactivity or physical properties. There are several topological indices have been defi ned on graphs using degrees of vertices/edges, for instance fi rst and second Zagreb indices. In this paper, we introduce a new topological index for graphs called Tosha index using tension on edges. Further, we establish some inequalities and compute Tosha index for some standard graphs.

참고문헌 (10)

  1. F. Harary, "Graph theory" (1972), Addison Wesley
  2. K. Bhargava, "Tension on an edge in a graph, Communicated for publication", ~
  3. I. Gutman, "Graph theory and molecular orbitals. Total n-electron energy of alternant hydrocarbons", Chem. Phys. Lett., 17, pp.535~538 (1972)
  4. I. Gutman, "Graph theory and molecular orbitals. XII. Acyclic polyenes", J. Chem. Phys., 62, pp.3399~3405 (1975)
  5. V. Lokesha, "New results on the F-index of graphs based on Corona-type products of graphs", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 23(2), pp.141~148 (2020), 장전수학회
  6. R. Rajendra, "Tosha-degree of an edge in a graph", Southeast Asian Bull. Math., 45 (2021)
  7. R. Rajendra, "On Tosha-degree of an edge in a graph", Eur. J. Pure Appl. Math., 13(5), pp.1097~1109 (2020)
  8. R. Rajendra, "Tosha-degree equivalence signed graphs", Vladikavkaz Math. J., 22(2), pp.48~52 (2020)
  9. K. B. Sudhakara, "Some edge degree based topological indices of graphene", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 23(2), pp.258~270 (2020), 장전수학회
  10. Aysun YURTTAS, "Zagreb indices of graphs with added edges", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 21(3), pp.385~392 (2018), 장전수학회[DOI]

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