We give a novel upper bound on graph energy in terms of the vertex cover number, and present a complete characterization of the graphs whose energy equals twice their matching number.
The irregularity of a graph is defined as the sum of imbalances over all edges , where denotes the degree of the vertex in . This graph invariant, introduced by Albertson in 1997, is a measure of the defect of regularity of a graph. In this paper, we completely determine the extremal values of the irregularity of connected graphs with vertices and pendant vertices (), and characterize the corresponding extremal graphs.
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