A simple graph G is said to be regular if its vertices have the same number of neighbors. Otherwise, id="M2"> nonregular. So far, various formulas, such as Albertson index, total and degree deviation, been introduced quantify irregularity a graph. In this paper, we present sharp lower bounds for these indices in terms or...

A hypergraph is k-irregular if there is no set of k vertices all of which have the same degree. We asymptotically determine the probability that a random uniform hypergraph is k-irregular.

Let G = (V,E), V = {1,2, . . . ,n}, be a simple graph without isolated vertices, with vertex degree sequence d1 ≥ d2 ≥ ·· · ≥ dn > 0, di = d(i). A graph G is regular if and only if d1 = d2 = · · · = dn. A graph invariant I(G) is measure of irregularity of graph G with the property I(G) = 0 if and only ifG is regular, and I(G)> 0 otherwise. In this paper we introduce some new irregularity measures.

In aortic stenosis, systemic arterial peak systolic pressure may remain relatively steady in the face of marked, arrhythmia-induced, variations in left ventricular peak systolic pressure. A possible basis for this phenomenon is presented. It is suggested that beat-tobeat variations in the systolic pressure gradient across the aortic valve region may not always reflect variations in stroke volume.

It is an elementary exercise to show that any non-trivial simple graph has two vertices with the same degree. This is not the case for digraphs and multigraphs. We consider generating irregular digraphs from arbitrary digraphs by adding multiple arcs. To this end, we define an irregular labeling of a digraph D to be an arc labeling of the digraph such that the ordered pairs of the sums of the i...