On graphs with signed inverses

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1988 English Publisher:WileyJournal:Networks, volume 18, pages 151-157 (issn: 0028-3045, eissn: 1097-0037,

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Authors: Fred Buckley; Lynne L. Doty; Frank Harary;

doi: 10.1002/net.3230180302

On graphs with signed inverses

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Abstract

AbstractA graph G is called invertible if its adjacency matrix A has an inverse which is the adjacency matrix of some graph H. All such graphs were shown by Harary and Minc to have the form nK2. We now introduce signed invertible (or briefly s‐invertible) graphs G as those whose inverse H is a signed graph. We identify two infinite classes of s‐invertible graphs: the paths P2n of even order, and the corona of any graph with K1. We then characterize s‐invertible trees.

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Keywords

Graph theory, signed graph, adjacency matrix, Graphs and linear algebra (matrices, eigenvalues, etc.), invertible graphs

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