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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.
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.
The simplest way to perform fuzzy risk assessment is to calculate the fuzzy expected value and convert fuzzy risk into non-fuzzy risk, converting it to a clear number. In doing so, there is a transition from a fuzzy set to clear set. Under such an a level, three risk values can be calculated. As adopts all values throughout the set, it is possible to obtain… (More)
In this paper, we first give a relation between the adjacency spectral radius and the Q-spectral radius of a graph. Then using this result, we further give some new sharp upper bounds on the adjacency spectral radius of a graph in terms of degrees and the average 2-degrees of vertices. Some known results are also obtained.