sink location is considered as a basic service in geographic routing in wireless sensor networks. obtaining the location of sink node by source node using an efficient method with low complexity has always been a challenging issue in research. in this paper, a sink location algorithm based on fano plane is proposed. the research challenge is how to ensure the intersection of two slq and sla rou...

Sink location is considered as a basic service in geographic routing in wireless sensor networks. Obtaining the location of sink node by source node using an efficient method with low complexity has always been a challenging issue in research. In this paper, a sink location algorithm based on Fano plane is proposed. The research challenge is how to ensure the intersection of two SLQ (Location Q...

Let F be a binary clutter. We prove that if F is non-ideal, then either F or its blocker b(F) has one of L7,O5,LC7 as a minor. L7 is the non-ideal clutter of the lines of the Fano plane, O5 is the non-ideal clutter of odd circuits of the complete graph K5, and the two-point Fano LC7 is the ideal clutter whose sets are the lines, and their complements, of the Fano plane that contain exactly one ...

The complements of the perfect dominating sets of the n-cube, for n $ 8, are characterized as well as some outstanding vertex-spanning edge-partitions of them involving the Fano plane, as a contribution to the study of distancepreserving regular subgraphs of hypercubes.

We prove that a binary geometry of rank n {n > 2) not containing M(Ky and F-, (respectively, M(K5) and C10) as a minor has at most 3/i 3 (respectively, 4« 5) points. Here, M(K5) is the cycle geometry of the complete graph on five vertices, F-, the Fano plane, and C10 a certain rank 4 ten-point geometry containing the dual Fano plane F* as a minor. Our technique is elementary and uses the notion...

Let F 7 denote the Fano matroid and e be a xed element of F 7 .

In this paper, we prove that the family of Fano threefolds with Picard number one is birationally unbounded.

Ivan V. Iorsh,1 Ilya V. Shadrivov,2 Pavel A. Belov,1 and Yuri S. Kivshar1,2 1National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101, Russia 2Nonlinear Physics Center, Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory 0200, Australia (Received 2 September 2013; published 20 Nove...

The hypergraph of the Fano plane is the unique 3-uniform hypergraph with 7 triples on 7 vertices in which every pair of vertices is contained in a unique triple. This hypergraph is not 2-colorable, but becomes so on deleting any hyperedge from it. We show that taking uniformly at random a labeled 3-uniform hypergraph H on n vertices not containing the hypergraph of the Fano plane, H turns out t...