Graph Invertibility based on Drazin Invers

André Luis Andrejew Ferreira, Débora Marília Hauenstein, Guilherme Porto


LetG= (V(G), E(G)) be a graph with vertex setV(G) ={v1, ..., vn}and edge setE(G). Inthis work, graphs may contain loops (edges that connects a vertex to itself) but no multiple edges.A weighted graph is a graph in which a number (the weight) is assigned to each edge. Let(G, w) be a weighted graph, wherew:E(G)→R\ {0}is the function that assigns weights tothe edges. The weighted adjacency matrix of (G, w) isA(G, w) = [aij], whereaij=w(vivj) ifvivj∈E(G) andaij= 0 otherwise. If the weight of each edge is equal to one thenA(G, w) is thestandard adjacency matrix of the graphG, denoted byA(G). [...]

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