Muhuo Liu

TL;DR: In this article, the authors present a survey on graphs extremal with respect to distance-based indices, with emphasis on the Wiener index, hyper-Wiener index and the Harary index.

TL;DR: In this paper, the signless Laplacian spread of G is defined as SQ(G ) = μ 1 (G ) − μ n (G ), where μ 1 and μ n are the maximum and minimum eigenvalues of G, respectively.

TL;DR: A sharp upper bound for the algebraic connectivity of a graph is obtained, and all the Laplacian integral unicyclic, bicyclic graphs are identified and determined by their LaPLacian spectra.

TL;DR: An extremal unicyclic graph is characterized that achieves the maximum second Zagreb index in the class of unicyCLic graphs with given degree sequence and it is proved that if @[email protected][email protected]^', @p and @p^' are unicyClic degree sequences and U^* and U*^* have the maximumsecond Zag Croatia indices in @C(@p) and @C (@p^'), respectively, then

TL;DR: It is shown that for positive integers s and t, g ( s , t ) ≤ s + t on ( K 4 − e ) -free graphs except K 3 , and for integers s ≥ 2 and t ≥ 2, g( s, t) ≤ s - t − 1 on triangle-free graphs in which no two quadrilaterals share edges.