Renying Chang

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The harmonic index H(G) of a graph G is defined as the sum of weights 2 d(u)+d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we have determined the minimum and maximum harmonic indices of bicyclic graphs and characterized the corresponding graphs at which the extremal harmonic indices are attained.
We say that a simple graph G is fractional independent-set-deletable k-factor-critical, shortly, fractional ID-k-factor-critical, if G− I has a fractional k-factor for every independent set I of G. Some sufficient conditions for a graph to be fractional ID-k-factor-critical are studied in this paper. Furthermore, we show that the result is best possible in(More)
Let S be a finite set of positive integers. A mixed hypergraph H is a onerealization of S if its feasible set is S and each entry of its chromatic spectrum is either 0 or 1. In [P. Zhao, K. Diao, Y. Chang and K. Wang, The smallest one-realization of a given set II, Discrete Math. 312 (2012) 2946–2951], we determined the minimum number of vertices of a(More)
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