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The convex linear combinations $D_{\\alpha}(G)$ of $Tr(G)$ and $D(G)$ is defined as $D_{\\alpha}(G)=\\alpha Tr(G)+(1-\\alpha)D(G)$, $0\\leq \\alpha\\leq 1$. As $D_{0}(G)=D(G), ~~~ 2D_{\\frac{1}{2}}(G)=D^{Q}(G), ~~~ D_{1}(G)=Tr(G)$ and $D_{\\alpha}(G)-D_{\\beta}(G)=(\\alpha-\\beta)D^{L}(G)$, this matrix reduces to merging the distance spectral, distance Lapl"},"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":"1907.09462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-22T17:55:42Z","cross_cats_sorted":[],"title_canon_sha256":"4681a2311378316f55b74a52ba2d9e2f3b8eabf896301115345a5e78bdbdd961","abstract_canon_sha256":"329d0863aef03575e503011eb6af493d0568ee6596b27cdfde92cfe346ca5b69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:59.166907Z","signature_b64":"ULXxbhEaiv2PS7yZJEzjQCfvq/9I7Gp6c3dqyUUz++la8Bp2EkGsa2Jfg8n1eL+UNVoemTfVYG8R6MhlQJI5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"738f0727ac63aee0c313657887cc2c36a50beb4dcb101dc987f5c202a3944615","last_reissued_at":"2026-05-17T23:39:59.166386Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:59.166386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On spectral spread of generalized distance matrix of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Alhevaz, Hilal A. Ganie, M. Baghipur, S. Pirzada","submitted_at":"2019-07-22T17:55:42Z","abstract_excerpt":"For a simple connected graph $G$, let $D(G)$, $Tr(G)$, $D^{L}(G)$ and $D^{Q}(G)$, respectively be the distance matrix, the diagonal matrix of the vertex transmissions, distance Laplacian matrix and the distance signless Laplacian matrix of a graph $G$. The convex linear combinations $D_{\\alpha}(G)$ of $Tr(G)$ and $D(G)$ is defined as $D_{\\alpha}(G)=\\alpha Tr(G)+(1-\\alpha)D(G)$, $0\\leq \\alpha\\leq 1$. As $D_{0}(G)=D(G), ~~~ 2D_{\\frac{1}{2}}(G)=D^{Q}(G), ~~~ D_{1}(G)=Tr(G)$ and $D_{\\alpha}(G)-D_{\\beta}(G)=(\\alpha-\\beta)D^{L}(G)$, this matrix reduces to merging the distance spectral, distance Lapl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09462","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.09462","created_at":"2026-05-17T23:39:59.166480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.09462v1","created_at":"2026-05-17T23:39:59.166480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09462","created_at":"2026-05-17T23:39:59.166480+00:00"},{"alias_kind":"pith_short_12","alias_value":"OOHQOJ5MMOXO","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"OOHQOJ5MMOXOBQYT","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"OOHQOJ5M","created_at":"2026-05-18T12:33:24.271573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2","json":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2.json","graph_json":"https://pith.science/api/pith-number/OOHQOJ5MMOXOBQYTMV4IPTBMG2/graph.json","events_json":"https://pith.science/api/pith-number/OOHQOJ5MMOXOBQYTMV4IPTBMG2/events.json","paper":"https://pith.science/paper/OOHQOJ5M"},"agent_actions":{"view_html":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2","download_json":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2.json","view_paper":"https://pith.science/paper/OOHQOJ5M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.09462&json=true","fetch_graph":"https://pith.science/api/pith-number/OOHQOJ5MMOXOBQYTMV4IPTBMG2/graph.json","fetch_events":"https://pith.science/api/pith-number/OOHQOJ5MMOXOBQYTMV4IPTBMG2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2/action/storage_attestation","attest_author":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2/action/author_attestation","sign_citation":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2/action/citation_signature","submit_replication":"https://pith.science/pith/OOHQOJ5MMOXOBQYTMV4IPTBMG2/action/replication_record"}},"created_at":"2026-05-17T23:39:59.166480+00:00","updated_at":"2026-05-17T23:39:59.166480+00:00"}