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We will use the graph theory to define the network.
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We describe those two structures using the graph theory concepts.
Connections between links are represented by using the graph theory.
The closed-loop systems are investigated using the graph theory, Lyapunov theory, and Barbalat lemma.
Furthermore, the paper gives the formal description for authorization division using the graph theory.
We have already used the graph theory concepts of path and cycle.
The optimal order of HAZOP nodes can be determined by using the graph theory and the matrix calculus.
Also, it is shown that using the graph theory greatly improves the convergence rate of the optimization.
By using the graph theory and the Lyapunov method, a Lyapunov-type theorem and some sufficient criteria are obtained.
By using the graph theory and theory of stochastic analysis, sufficient conditions of mean square containment control for multi-agent systems are derived.
Using the graph theory and Lyapunov methods, it is shown that the coupling gains will vanish when the multi-agent systems achieve consensus.
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