Author
Yuan Hong
Bio: Yuan Hong is an academic researcher from East China Normal University. The author has contributed to research in topics: Bound graph & Regular graph. The author has an hindex of 5, co-authored 5 publications receiving 359 citations.
Papers
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TL;DR: The following sharp upper bound is obtained of the minimum degree of vertices of G, which is either a regular graph or a bidegreed graph in which each vertex is of degree either ? or n?1.
157 citations
TL;DR: The following results are given: Let T be a tree with n vertices and k pendant vertices, where equality holds if and only if G is a regular connected bipartite graph.
145 citations
TL;DR: In this paper, several results are presented concerning bounds on the eigenvalues of G, and it is shown that −1⩽λ2(G) ⩽(n−2)/2, and the left hand equality holds if and only ifG is a complete graph with at least two vertices.
68 citations
TL;DR: A sharp upper bound of the Nordhaus–Gaddum type is obtained: ρ(G)+ρ(G c )⩽ 2− 1 k − 1 k n(n−1) , where k and k are the chromatic numbers of G and G c , respectively.
24 citations
TL;DR: In this paper, several results which are concerned with tree-width, clique-minors, and eigenvalues of graphs are given.
18 citations
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TL;DR: This is a bibliography of signed graphs and related mathematics, where work on weighted graphs are regarded as outside the scope of the bibliography — except (to some extent) when the author calls the weights "signs".
Abstract: A signed graph is a graph whose edges are labeled by signs. This is a bibliography of signed graphs and related mathematics. Several kinds of labelled graph have been called "signed" yet are mathematically very different. I distinguish four types: Group-signed graphs: the edge labels are elements of a 2-element group and are multiplied around a polygon (or along any walk). Among the natural generalizations are larger groups and vertex signs. Sign-colored graphs, in which the edges are labelled from a two-element set that is acted upon by the sign group: - interchanges labels, + leaves them unchanged. This is the kind of "signed graph" found in knot theory. The natural generalization is to more colors and more general groups — or no group. Weighted graphs, in which the edge labels are the elements +1 and -1 of the integers or another additive domain. Weights behave like numbers, not signs; thus I regard work on weighted graphs as outside the scope of the bibliography — ex cept (to some extent) when the author calls the weights "signs". Labelled graphs where the labels have no structure or properties but are called "signs" for any or no reason.
258 citations
TL;DR: It is shown that if G is Kp+1-free then if δ be the minimal degree of G then This inequality supersedes inequalities of Stanley and Hong and is sharp for regular graphs and for a class of graphs which are in some sense maximally irregular.
Abstract: Let λ(G) be the largest eigenvalue of the adjacency matrix of a graph G: We show that if G is Kp+1-free then ***** insert CODING here *****This inequality was first conjectured by Edwards and Elphick in 1983 and supersedes a series of previous results on upper bounds of λ(G).Let Ti denote the number of all i-cliques of G, λ = λ(G) and p = cl(G): We show ***** insert equation here *****Let δ be the minimal degree of G. We show ***** insert equation here *****This inequality supersedes inequalities of Stanley and Hong. It is sharp for regular graphs and for a class of graphs which are in some sense maximally irregular.
202 citations
TL;DR: In this article, a survey of properties of spectra of signless Laplacians of graphs is presented, and the main result concerns the graphs whose largest eigenvalue is maximal among the graphs with fixed numbers of vertices and edges.
Abstract: We extend our previous survey of properties of spectra of signless Laplacians of graphs. Some new bounds for eigenvalues are given, and the main result concerns the graphs whose largest eigenvalue is maximal among the graphs with fixed numbers of vertices and edges. The results are presented in the context of a number of computer-generated conjectures.
199 citations
TL;DR: In this paper, Nordhaus and Gaddum gave lower and upper bounds on the sum and product of the chromatic number of a graph and its complement, in terms of the order of the graph.
198 citations
TL;DR: In this paper, the spectral radius of the adjacency matrix and the Laplacian matrix of a simple undirected graph is analyzed in terms of the degrees and the 2-degrees of vertices.
161 citations