Displaying similar documents to “The Spectrum Of Line Graphs Of Some Infinite Graphs”

Per-Spectral Characterizations Of Some Bipartite Graphs

Tingzeng Wu, Heping Zhang (2017)

Discussiones Mathematicae Graph Theory

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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

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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...

On some characterizations of strong power graphs of finite groups

A. K. Bhuniya, Sudip Bera (2016)

Special Matrices

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Let G be a finite group of order n. The strong power graph Ps(G) of G is the undirected graph whose vertices are the elements of G such that two distinct vertices a and b are adjacent if am1=bm2 for some positive integers m1, m2 < n. In this article we classify all groups G for which Ps(G) is a line graph. Spectrum and permanent of the Laplacian matrix of the strong power graph Ps(G) are found for any finite group G.