{"paper":{"title":"Some New Results on Integer Additive Set-Valued Signed Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"K. A. Germina, N. K. Sudev, P. K. Ashraf","submitted_at":"2016-09-01T16:05:23Z","abstract_excerpt":"Let $X$ denotes a set of non-negative integers and $\\mathscr{P}(X)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\\to \\mathscr{P}(X)-\\{\\emptyset\\}$ such that the induced function $f^+:E(G) \\to \\mathscr{P}(X)-\\{\\emptyset\\}$ is defined by $f^+(uv)=f(u)+f(v);\\ \\forall\\, uv\\in E(G)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. An IASL of a signed graph is an IASL of its underlying graph $G$ together with the signature $\\sigma$ defined by $\\sigma(uv)=(-1)^{|f^+(uv)|};\\ \\forall\\, uv\\in E(\\Sigma)$. In this paper, we discu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00295","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"}