Given a graph G, a function f : V (G)→ {1, 2, ..., k} is a k-biranking of G if f(u) = f(v) implies every u-v path contains vertices x and y such that f(x) > f(u) and f(y) < f(u). The birank number of a graph, denoted bi(G), is the minimum k such that G has a k-biranking. In this paper we determine the birank numbers for ladder, prism, and Möbius ladder graphs.

In this article we compute analytically the number of Nash Equilibria (NE) for a two-choice game played on (circular) ladder graph with $2n$ players. We consider set games generic payoff parameters, only requirement that NE occurs if players choose opposite strategies (anti-coordination game). The results show both, and circular ladder, grows exponentially (half) $n$, as $N_{NE}(2n)\sim C(\varp...

Smac/DIABLO, HtrA2/Omi, and caspase-9 play key roles in the initiation of apoptosis. The inhibitor of apoptosis proteins (IAPs) are believed to bind to the N-terminal IAP binding motifs of the mature (proteolytically processed) forms of Smac, HtrA2, and caspase-9. However, we show here that BRUCE/Apollon, a 528-kDa IAP whose degradation promotes apoptosis, associates with their precursors as we...