Displaying similar documents to “The algebraic multiplicity of the number zero in the spectrum of a bipartite graph”

Per-Spectral Characterizations Of Some Bipartite Graphs

Tingzeng Wu, Heping Zhang (2017)

Discussiones Mathematicae Graph Theory

Similarity:

A graph is said to be characterized by its permanental spectrum if there is no other non-isomorphic graph with the same permanental spectrum. In this paper, we investigate when a complete bipartite graph Kp,p with some edges deleted is determined by its permanental spectrum. We first prove that a graph obtained from Kp,p by deleting all edges of a star K1,l, provided l < p, is determined by its permanental spectrum. Furthermore, we show that all graphs with a perfect matching obtained...

Saturation Spectrum of Paths and Stars

Jill Faudree, Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson, Brent J. Thomas (2017)

Discussiones Mathematicae Graph Theory

Similarity:

A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from G̅ to G results in a copy of H. The minimum size of an H-saturated graph on n vertices is denoted sat(n,H), while the maximum size is the well studied extremal number, ex(n,H). The saturation spectrum for a graph H is the set of sizes of H saturated graphs between sat(n,H) and ex(n,H). In this paper we completely determine the saturation spectrum of stars and we show the saturation spectrum of paths...