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Similarly, $D \\subset V(G)$ is a non-porous exponential dominating set is $1\\le \\sum_{d \\in D} \\left( \\frac{1}{2} \\right)^{\\overline{\\text{dist}}(d,v) -1}$ for every $v \\in V(G),$ where $\\overline{\\text{dist}}(d,v)$ represents the length of the shortest $dv$ path with no internal vertices in $D.$ The porous and non-porous exponential dominating n"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.05429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-14T19:49:07Z","cross_cats_sorted":[],"title_canon_sha256":"c2d4916127cd60ca325cfafd8aaf2f26a264e67cafee6cb3f8de2caa8fd8b36f","abstract_canon_sha256":"f7a863f37cd3630f075e2c29c9df01a61b9586cab203bcbc21c040ccf05ae856"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:56.499820Z","signature_b64":"dClvzyJse2zOTAxhwCTBTVtWXGHSuYXV2R+XRsHuRkvZEAFyTVZlVeG38lCHtikQQzCV/9CwzlXpg2gaERUqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"936c30d7de150e94ecab33f3d82be1c49463c595645b519630d0cf85e631c705","last_reissued_at":"2026-05-18T00:27:56.499132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:56.499132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On exponential domination of the consecutive circulant graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Dairyko, Michael Young","submitted_at":"2017-12-14T19:49:07Z","abstract_excerpt":"For a graph $G,$ we consider $D \\subset V(G)$ to be a porous exponential dominating set if $1\\le \\sum_{d \\in D}$ $\\left( \\frac{1}{2} \\right)^{\\text{dist}(d,v) -1}$ for every $v \\in V(G),$ where dist$(d,v)$ denotes the length of the smallest $dv$ path. 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