Isolated toughness and fractional (k; m)--covered graph

Articles in Press

Document Type : Research Paper

Authors

1 School of Mathematics, Hohai University, Nanjing 211100, China.

2 Engineering School (DEIM), University of Tuscia, Viterbo 01100, Italy.

3 Università degli Studi di Messina, Dipartimento di Scienze Biomediche, Odontoiatriche e delle Immagini Morfologiche e Funzionali, Messina, 98122, Italy.

4 Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa 63159, Turkey.

Abstract

The fractional k-factor is a spanning subgraph determined by the support set of the fractional
indicator function, which requires that the sum of the fractional indicator function values of the
edges incident with each vertex is k, where k is a positive integer. A graph G is fractional
(k; m)-covered if for any H ⊆ E(G) with jHj = m, there is a fractional factor with fractional
indicator function h satisfying h(e) = 1 for any e 2 H. Isolated toughness is a pivotal indicator
in network security and a prominent performance indicator that engineers considering during
the network design phase. In this work, we present the isolated toughness and its variant
bounds for fractional (k; m)-covered graphs, and the sharpness of given bounds are delineated
by counterexamples.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 05 June 2026

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History

  • Receive Date: 05 July 2025
  • Revise Date: 15 April 2026
  • Accept Date: 03 June 2026

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