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Construction of larger singular and nonsingular graphs using a path
<span title="">2020</span>
<i title="Malaya Journal of Matematik">
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A singular graph G has an adjacency matrix A(G) with nullity η(G) > 0. Vertices of singular graphs are classified as core and noncore vertices. There are two types of noncore vertices: noncore vertices of zero null spread and of null spread −1. Deletion of these vertices from a singular graph either changes the nullity or leave it unaltered. In this paper larger singular and nonsingular graphs were constructed by joining singular graphs by a path. As singular graphs have different types of
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... ces, the graphs constructed in this way differ in nullity depending on the vertex we are joining during construction. An attempt was made to construct singular graph of maximum nullity. Various spectral properties of the resulting graphs were studied.
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