How to compute the M-polynomial of (chemical) graphs

Deutsch, Emeric (author), Klavžar, Sandi (author), Romih, Gašper Domen (author)

Let $G$ be a graph and let $m_{i,j}(G)$, $i,j\ge 1$, be the number of edges $uv$ of $G$ such that $\{d_v(G), d_u(G)\} = \{i,j\}$. The M-polynomial of $G$ is $M(G;x,y) = \sum_{i\le j} m_{i,j}(G)x^iy^j$. A general method for calculating the M-polynomials for arbitrary graph families is presented. The method is further developed for the case where the vertices of a graph have degrees $2$ and $p$, where $p\ge 3$, and further for such planar graphs. The method is illustrated on families of chemical graphs.

• Language: English
• Keywords: M-polynomial, chemical graph, planar graph
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2023
• Year: 2023
• Number of pages: Str. 275-285
• Numbering: Vol. 89, no. 2
• PID: 20.500.12556/RUL-155059
• UDC: 519.17:54
• ISSN on article: 0340-6253
• DOI: 10.46793/match.89-2.275D
• COBISS.SI-ID: 118666243
• Publication date in RUL: 18.03.2024

Record is a part of a journal

• Title: Match. communications in mathematical and in computer chemistry
• Shortened title: Match
• Publisher: University of Kragujevac, Faculty of Science
• ISSN: 0340-6253
• COBISS.SI-ID: 2624551

Secondary language

• Language: Slovenian
• Keywords: M-polinom, kemijski graf, ravninski graf