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- W1971681567 abstract "The Randić index R of a graph G is defined as the sum of (didj)−12 over all edges vivj of G, where di denotes the degree of a vertex vi in G. q1 is the largest eigenvalue of the signless Laplacian matrix Q=D+A of G, where D is the diagonal matrix with degrees of the vertices on the main diagonal and A is the adjacency matrix of G. Hansen and Lucas [18] conjectured (1) q1−R⩽32n−2 and equality holds for G≅Kn and (2)q1R⩽{4n−4n,4⩽n⩽12,nn−1,n⩾13 with equality if and only if G≅Kn for 4⩽n⩽12 and G≅Sn for n⩾13, respectively. In this paper, we prove the conjecture (1) and obtain a result very close to the conjecture (2). Moreover, we give some results relating harmonic index and the largest eigenvalue of the adjacency matrix." @default.
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- W1971681567 date "2014-03-01" @default.
- W1971681567 modified "2023-09-24" @default.
- W1971681567 title "On two conjectures of Randić index and the largest signless Laplacian eigenvalue of graphs" @default.
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- W1971681567 doi "https://doi.org/10.1016/j.jmaa.2013.09.014" @default.
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