{"paper":{"title":"M-Polynomial Revisited: Bethe Cacti and an Extension of Gutman's Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emeric Deutsch, Sandi Klav\\v{z}ar","submitted_at":"2018-06-21T11:51:06Z","abstract_excerpt":"The $M$-polynomial of a graph $G$ is defined as $\\sum_{i\\le j} m_{i,j}(G)x^iy^j$, where $m_{i,j}(G)$, $i,j\\ge 1$, is the number of edges $uv$ of $G$ such that $\\{d_v(G), d_u(G)\\} = \\{i,j\\}$. Knowing the $M$-polynomial, formulas for bond incident degree indices (an important subclass of degree-based topological indices) can be obtained by means of specific operators defined on differentiable functions in two variables. This is illustrated on three infinite families of Bethe cacti. Gutman's approach for the computation of the coefficients of the $M$-polynomial is also recalled and an extension o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08183","kind":"arxiv","version":2},"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"}