vol1_pp34-43. 168KB Jun 04 2011 12:06:06 AM
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If there are two vertices on the 3-cycle which are adjacent to pendant vertices, then by considering Perron components, we nd that Case A holds, with the 3-cycle as the unique
In this paper, quite tight lower and upper bounds are obtained on the algebrai on- netivity, namely , the seond-smallest eigenvalue of the Laplaian matrix, of an unweighted
It was provedfor triangle free graphs in [11], for graphs which contain no odd cycle on 5 or more vertices in [10], for all graphs on 5 vertices which are not the complete graph
In this paper, the trees with a given diameter having the minimal energy are determined by three specific tree operations; using this method, together with previous work, a
Zero-nonzero patterns, Nilpotent, Ideal saturation, Gr¨ obner basis, Finite fields.. AMS
Minimum semidefinite rank, Minimum vector rank, Duplicate vertices, Chordal graph.. AMS
, n is called a recursive tree if the vertex labelled 1 is the root and, for all 2 ≤ k ≤ n, the sequence of vertex labels in the path from the root to k is increasing (Stanley
One example of a graph model for obtaining a prescribed degree distribution is the so called configuration model – see Molloy and Reed (1995,1998) – where, given n vertices, each
