On the Wiener index of two families generated by joining a graph to a tree Full article
| Journal |
Discrete Mathematics Letters
ISSN: 2664-2557 |
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| Output data | Year: 2022, Volume: 9, Pages: 44-48 Pages count : 5 DOI: 10.47443/dml.2021.s208 | ||
| Tags | Distance in graphs; Graph invariant; Wiener index | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
The Wiener index W(G) of a graph G is the sum of distances between all vertices of G. The Wiener index of a family of connected graphs is defined as the sum of the Wiener indices of its members. Two families of graphs can be constructed by identifying a fixed vertex of an arbitrary graph F with vertices or subdivision vertices of an arbitrary tree T of order n. Let Gv be a graph obtained by identifying a fixed vertex of F with a vertex v of T. The first family V = {Gv | v ∈ V (T)} contains n graphs. Denote by Gve a graph obtained by identifying the same fixed vertex of F with the subdivision vertexve of an edge e in T. The second family ε = {Gve | e ∈ E(T)} contains n - 1 graphs. It is proved that W(V) = W(ε) if and only if W(F) = 2W(T).
Cite:
Dobrynin A.A.
On the Wiener index of two families generated by joining a graph to a tree
Discrete Mathematics Letters. 2022. V.9. P.44-48. DOI: 10.47443/dml.2021.s208 WOS Scopus РИНЦ OpenAlex
On the Wiener index of two families generated by joining a graph to a tree
Discrete Mathematics Letters. 2022. V.9. P.44-48. DOI: 10.47443/dml.2021.s208 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000894319900008 |
| Scopus: | 2-s2.0-85126646641 |
| Elibrary: | 48194240 |
| OpenAlex: | W4210657334 |