The Extension Degree Conditions for Fractional Factor

Gao, Wei; Wang, Wei Fan; Guirao, Juan Luis García

doi:10.1007/s10114-020-9156-0

Cited by 12 publications

(6 citation statements)

References 17 publications

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“…Studies in the past 10 years have shown that these three parameters characterize the vulnerability of a network, the existence of factors and fractional factors which represent the feasibility of data transmission (see Gao et al [19][20][21], and also path factor-a special class of the factor (see Zhou et al 22,23 ). In particular, several network robustness parameter conditions with regard to path factors have been obtained in the recent past 2 years.…”

Section: Motivationmentioning

confidence: 99%

Tight bounds for the existence of path factors in network vulnerability parameter settings

2020

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The issues of ruggedness and vulnerability are cruxes in network security research, which must be considered during the network designing phase. Parameters such as toughness, isolated toughness, and binding number characterize the vulnerable of the network from the structure of networks. The path factor, a special case of the generalized MJX-tex-caligraphicnormalℋ‐factor, measures the feasibility of data transmission in networks. Recent advances have been obtained to show that there is an inevitable connection between the vulnerability parameters of the network and the existence of path factors, while we found that some existing theoretical results are not tight and there is still a long way for further improvement. In view of graph theory approaches, this paper mainly contributes to determine the sharp bounds of toughness, isolated toughness, and binding number for the existence of path factor in different settings, and therefore solve the open problems left unsolved in previous articles.

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Section: Motivationmentioning

confidence: 99%

Tight bounds for the existence of path factors in network vulnerability parameter settings

2020

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“…If S is an empty set, then using (9), we have i(G ′ ) ≥ 1 which contradicts to G is 2-edge-connected. Assume that |S| � 1. en, ε 1 (S) ≤ 1, and hence i(G ′ − S) ≥ 2 in light of (9). We get i(G − S) � 0 since G is 2-edgeconnected.…”

Section: Factor Uniform Graphmentioning

confidence: 84%

“…Some recent advances in graph factors can be referred to Zhou et al [6] and Gao et al [7][8][9]. e main contribution in this work is to study the existence of P ≥2 -factor or P ≥3 -factor in special settings by means of sun toughness parameter.…”

Section: Introductionmentioning

confidence: 99%

Sun Toughness Conditions for $P_{2}$ and

Gong

Baskonus

Gao

2021

Journal of Mathematics

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The security of a network is closely related to the structure of the network graph. The denser the network graph structure is, the better it can resist attacks. Toughness and isolated toughness are used to characterize the vulnerable programs of the network which have been paid attention from mathematics and computer scholars. On this basis, considering the particularity of the sun component structures, sun toughness was introduced in mathematics and applied to computer networks. From the perspective of modern graph theory, this paper presents the sun toughness conditions of the path factor uniform graph and the path factor critical avoidable graph in P ≥ 2 -factor and P ≥ 3 -factor settings. Furthermore, examples show that the given boundaries are sharp.

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“…More recent results on graph factors in various settings can be referred to Gao et al [3,4], Wang and Zhang and Zhou et al [5][6][7][8][9][10], and Zhu et al [11,12].…”

Section: Introductionmentioning

confidence: 99%

Forbidden Restrictions and the Existence of $P_{\geq 2}$ -Factor and

Yuan

Baskonus

et al. 2023

Journal of Function Spaces

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The existence of factor and fractional factor in network graph in various settings has raised much attention from both mathematicians and computer scientists. It implies the availability of data transmission and network segmentation in certain special settings. In our paper, we consider P ≥ 2 -factor and P ≥ 3 -factor which are two special cases of general H -factor. Specifically, we study the existence of these two kinds of path factor when some subgraphs are forbidden, and several conclusions on the factor-deleted graph, factor critical-covered graph, and factor uniform graph are given with regards to network parameters. Furthermore, we show that these bounds are best in some sense.

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The Extension Degree Conditions for Fractional Factor

Cited by 12 publications

References 17 publications

Tight bounds for the existence of path factors in network vulnerability parameter settings

Tight bounds for the existence of path factors in network vulnerability parameter settings

Sun Toughness Conditions for $P_{2}$ and

Forbidden Restrictions and the Existence of $P_{\geq 2}$ -Factor and

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The Extension Degree Conditions for Fractional Factor

Cited by 12 publications

References 17 publications

Tight bounds for the existence of path factors in network vulnerability parameter settings

Tight bounds for the existence of path factors in network vulnerability parameter settings

Sun Toughness Conditions for P 2 and

Forbidden Restrictions and the Existence of P ≥ 2 -Factor and

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Product

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Sun Toughness Conditions for $P_{2}$ and

Forbidden Restrictions and the Existence of $P_{\geq 2}$ -Factor and