Let Γ denote a finite, connected, simple graph. For an edge e of let n(e) the number girth cycles containing e. vertex v {e1, e2, …, ek} be set edges incident to ordered such that n(e1) ≤ n(e2) … n(ek). Then (n(e1),n(e2),…,n(ek)) is called signature v. The graph said girth-biregular if it bipartite, and all its vertices belonging same bipartition have signature. with g = 2d signatures (a1,a2,…,...

BACKGROUND Physical inactivity, cigarette smoking, and abdominal obesity are key modifiable risk factors for coronary heart disease (CHD). We investigated the combined effects of not having these risk factors on CHD events and cardiovascular disease (CVD) and all-cause mortality in men. METHODS We followed up 23 657 men, aged 30 to 79 years, who completed a medical evaluation including a maxi...

42 JANUARY 2004 1053-5888/04/$20.00©2004IEEE e consider the problem of designing unoriented bipartite graphs with large girth. These graphs are the Tanner graphs associated with the parity-check matrix H of low density parity-check (LDPC) codes or Gallager codes. Larger girth improves the computational and bit error rate (BER) performance of these codes. The article overviews several existing m...

In this paper, a recursive algorithm is presented to generate some exponent matrices which correspond to Tanner graphs with girth at least 6. For a J × L exponent matrix E, the lower bound Q(E) is obtained explicitly such that (J, L) QC LDPC codes with girth at least 6 exist for any circulant permutation matrix (CPM) size m ≥ Q(E). The results show that the exponent matrices constructed with ou...

A 29-year-old female with adult-onset Still's disease (AOSD) presented with progressive shortness of breath both on rest and on exertion, increased abdominal girth, and swelling in both legs. She was on oral prednisone and was recently started on canakinumab (interleukin-1 antagonist) for joint pain and rash of AOSD. Echocardiogram showed severely dilated right ventricle, dilated pulmonary arte...

By a symmetric graph we mean a graph X which automorphism group acts transitively on the arcs of X. A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. Tutte [31, 32] showed that every finite symmetric cubic graph is s-regular for some s ≤ 5. It is well-known that there are precisely five symmetric cubic graphs of girth less than 6. All these graphs can be re...

We present a necessary and sufficient condition for a graph of odd-girth 2k + 1 to bound the class of K4-minor-free graphs of odd-girth (at least) 2k + 1, that is, to admit a homomorphism from any such K4-minor-free graph. This yields a polynomial-time algorithm to recognize such bounds. Using this condition, we first prove that every K4-minor free graph of odd-girth 2k+1 admits a homomorphism ...