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In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.
Male and female poplars (Populus cathayana Rehd.) respond differently to environmental stresses. However, little is known about sex-dependent responses to chilling at the proteome level. To better understand these differences, a comparative proteomics investigation combined with a biochemical approach was used in the current study. Three-month-old poplar… (More)
The connective eccentricity index of a graph G is defined as ξ ce (G) = v∈V (G) d(v) ε(v) , where ε(v) and d(v) denote the eccentricity and the degree of the vertex v, respectively. In this paper we derive upper or lower bounds for the connective eccentricity index in terms of some graph invariants such as the radius, independence number, vertex… (More)
We consider the set G n,k of graphs of order n with the chromatic number k ≥ 2. In this note, we prove that in G n,k the Turán graph T n,k has the maximal spectral radius; and P n if k = 2, C n if k = 3 and n is odd, C 1 n−1 if k = 3 and n is even, K (l) k if k ≥ 4 has the minimal spectral radius. Thus we answer a problem raised by Cao [D.
Let G be a connected graph with vertex set V .G/. is the degree of vertex u, and R.u; v/ denotes the resistance distance between vertices u and v. In this paper we obtain some upper and lower bounds for the degree Kirchhoff index of graphs. We also obtain some bounds for the Nordhaus-Gaddum-type result for the degree Kirchhoff index.