Maxima of the Q-index: graphs without long paths
نویسندگان
چکیده
This paper gives tight upper bound on the largest eigenvalue q (G) of the signless Laplacian of graphs with no paths of given order. Thus, let Sn,k be the join of a complete graph of order k and an independent set of order n− k, and let S n,k be the graph obtained by adding an edge to Sn,k. The main result of the paper is the following theorem: Let k ≥ 1, n ≥ 7k, and let G be a graph of order n. (i) If q (G) ≥ q (
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Ela Maxima of the Q-index: Graphs without Long Paths
This paper gives tight upper bound on the largest eigenvalue q (G) of the signless Laplacian of graphs with no paths of given order. Thus, let Sn,k be the join of a complete graph of order k and an independent set of order n− k, and let S n,k be the graph obtained by adding an edge to Sn,k. The main result of the paper is the following theorem: Let k ≥ 1, n ≥ 7k, and let G be a graph of order n...
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