Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounding the Porous Exponential Domination Number of Apollonian Networks   Given a graph G with vertex set V, a subset S of V is a dominating set if
every vertex in V is either in S or adjacent to some vertex in S. The size of a
smallest dominating set is called the domination number of G. We study a
variant of domination called porous exponential domination in which each vertex
v of V is assigned a weight by each vertex s of S that decreases exponentially
as the distance between v and s increases. S is a porous exponential dominating
set for G if all vertices in S distribute to vertices in G a total weight of at
least 1. The porous exponential domination number of G is the size of a
smallest porous exponential dominating set. In this paper we compute bounds for
the porous exponential domination number of special graphs known as Apollonian
networks.

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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin