Abstract
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 inP≥2-factor andP≥3-factor settings. Furthermore, examples show that the given boundaries are sharp.
Highlights
Network security is one of most important focus points in computer networks
We only discuss the theoretical problems in computer network such that all network structures are denoted by graphs, and only simple graphs are considered. at is to say, if there are multiple channels connected between two sites, the model will be idealized, thinking that only one edge connects two corresponding vertices
We study the sun toughness condition for path factor uniform graphs
Summary
Network security is one of most important focus points in computer networks. When the network is represented by a graph model, graph parameters are introduced to describe the stability and vulnerability of the network under a specific structure. e classic parameters to measure the vulnerability of a network include toughness, isolated toughness, and binding number. We study the sun toughness condition for path factor uniform graphs. We confirm that G is a graph which is obtained by inserting an edge in a big sun.
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