M-Polynomial of Product Graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918383230910464 |
|---|---|
| author | Mehiri, El-Mehdi Klavžar, Sandi |
| author_facet | Mehiri, El-Mehdi Klavžar, Sandi |
| contents | The M-polynomial provides a unifying framework for a wide class of degree-based topological indices. Despite its structural importance, general methods for computing the M-polynomial under graph constructions remain limited. In this paper, explicit formulas, and compact ones whenever possible, for the M-polynomial under different graph products whose vertex sets are the Cartesian product of the factors are developed. The products studied are the direct, the Cartesian, the strong, the lexicographic, the symmetric-difference, the disjunction, and the Sierpiński product. The obtained formulas yield a unified structural description of how vertex-degree interactions propagate under graph constructions and extend existing results for degree-based indices at the polynomial level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10596 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | M-Polynomial of Product Graphs Mehiri, El-Mehdi Klavžar, Sandi Combinatorics Discrete Mathematics 05C31, 05C09, 05C76, 05C92, 05A15 The M-polynomial provides a unifying framework for a wide class of degree-based topological indices. Despite its structural importance, general methods for computing the M-polynomial under graph constructions remain limited. In this paper, explicit formulas, and compact ones whenever possible, for the M-polynomial under different graph products whose vertex sets are the Cartesian product of the factors are developed. The products studied are the direct, the Cartesian, the strong, the lexicographic, the symmetric-difference, the disjunction, and the Sierpiński product. The obtained formulas yield a unified structural description of how vertex-degree interactions propagate under graph constructions and extend existing results for degree-based indices at the polynomial level. |
| title | M-Polynomial of Product Graphs |
| topic | Combinatorics Discrete Mathematics 05C31, 05C09, 05C76, 05C92, 05A15 |
| url | https://arxiv.org/abs/2603.10596 |