The Exact Controllability of the Molecular Graph Networks

Abstract

In this paper, we mainly study the exact controllability of several types of extended-path molecular graph networks. Based on the construction of extended-path molecular graph networks with C 3 , C 4 , or K 4 , using the determinant operation of the matrix and the recursive method, the exact characteristic polynomial of these networks is deduced. According to the definition of minimum driver node number N D , the exact controllability of these networks is obtained. Moreover, we give the minimum driver node sets of partial small networks.

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“…6% nodes are very Enough to control the metabolic network [12], [22].of the entire network system quantitatively [23], [3]. They used the driving node method D N to calculate control by this equation [26] represent the whole nodes of the network [24] Where ( ) = rank [ ( ) ( ) 2 ( ) ( )] -Maximum Matching & Driver Nodes Maximum matching means the maximum group of links that no share starts or end nodes in the Bipartite-graph. Driver nodes (D N ) means a node that shares links [4] if the network is perfectly matched then the number of D is 1; otherwise [26] , , where N is the number of matched nodes, N is the whole number of nodes [25] [26], [27], [22][6].…”