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In an EC code, the overlapping between chunks is generated using a regular graph: each chunk corresponds to a node in the graph and two adjacent chunks share an input packet.
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Therefore, for any ℓ, one can design a code using a regular bipartite graph from [15] which ensures cooperative local repair of any ℓ erasures.
Using a regular toaster?
Within each graph, two A-scans are displayed, which were calibrated and retrieved through different optical frequency clock signal: the dash line represents using a regular MZI clock; Solid line represents using a log-amplified MZI clock.
Note that Theorem 2 establish that the code ({mathcal C}) obtained using a Δ-regular graph with girth g has ((g−1)(Δ−1),g−1 -cooperative locality.
Let G= V,E) be a regular graph of valency d.
An n-dimensional Bijective Connection graph (in brief BC graph) is a regular graph with 2n nodes and n2n−1 edges.
And the equality holds if and only if G is a regular graph or a bipartite semi-regular graph.
And the equality holds in (15) for regular graphs if and only if G is a regular graph.
A graph G is k-regular if (d v) = k) for all (v in V(G)) ; a regular graph is one that is k-regular for some k.
In this section, we investigate IE of line graph, subdivision graph, para-line graph and total graph of a regular graph.
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