![]() This algorithm can be used to determine if a graph G with a terminal vertex is not a NSSD. Moreover, an algorithm yielding what we term plain NSSDs is presented. It is shown that a necessary and sufficient condition for two–vertex deleted subgraphs of G and of the graph ⌈(G−1) associated with G−1 to remain NSSDs is that the submatrices belonging to them, derived from G and G−1, are inverses. We present results on the nullities of one– and two–vertex deleted subgraphs of a NSSD. We show that the class of NSSDs is closed under taking the inverse of G. A graph associated with a n × n non–singular matrix with zero entries on the diagonal such that all its (n − 1) × (n − 1) principal submatrices are singular is said to be a NSSD. TY - JOUR AU - Alexander Farrugia AU - John Baptist Gauci AU - Irene Sciriha TI - On the inverse of the adjacency matrix of a graph JO - Special Matrices PY - 2013 VL - 1 SP - 28 EP - 41 AB - A real symmetric matrix G with zero diagonal encodes the adjacencies of the vertices of a graph G with weighted edges and no loops. Moreover, an algorithm yielding what we term plain NSSDs is presented. The adjacency matrix, also called the connection matrix, is a matrix containing rows and columns which is used to represent a simple labelled graph, with 0 or 1 in the position of (V i, V j) according to the condition whether V i and V j are adjacent or not. ![]() On the inverse of the adjacency matrix of a graphĪlexander Farrugia John Baptist Gauci Irene ScirihaĪ real symmetric matrix G with zero diagonal encodes the adjacencies of the vertices of a graph G with weighted edges and no loops.
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