Critical Graphs in Index Coding


During this paper, we tend to define essential graphs as minimal graphs that support a given set of rates for the index coding downside and study them for both the one-shot and asymptotic setups. For the case of equal rates, we tend to realize the essential graph with minimum range of edges for each one-shot and asymptotic cases. For the overall case of presumably distinct rates, we have a tendency to show that for one-shot and asymptotic linear index coding, along with asymptotic nonlinear index coding, every crucial graph is a union of disjoint strongly connected subgraphs. On the other hand, we have a tendency to identify a non-USCS important graph for a one-shot nonlinear index coding problem. Next, we have a tendency to identify some graph structures that are important. As well, we have a tendency to show that the capacity region of the index coding is additive for union of disjoint graphs.

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