The clique number and the smallest Q-eigenvalue of graphs
نویسندگان
چکیده
Let qmin(G) stand for the smallest eigenvalue of the signless Laplacian of a graph G of order n: This paper gives some results on the following extremal problem: How large can qmin (G) be if G is a graph of order n; with no complete subgraph of order r + 1? It is shown that this problem is related to the well-known topic of making graphs bipartite. Using known classical results, several bounds on qmin are obtained, thus extending previous work of Brandt for regular graphs. In addition, using graph blowups, a general asymptotic result about the maximum qmin is established. As a supporting tool, the spectra of the Laplacian and the signless Laplacian of blowups of graphs are calculated. Keywords: blow-up graphs; Laplacian; signless Laplacian; complete subgraphs; extremal problem, clique number. AMS classi cation: 05C50
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 339 شماره
صفحات -
تاریخ انتشار 2016