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Extremal structures of graphs with given connectivity or number of pendant vertices
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wang, Shaohui Ji, Shengjin Muche, Tilahun Hayat, Sakander |
| Copyright Year | 2017 |
| Abstract | For a graph $G$, the first multiplicative Zagreb index $\prod_1(G) $ is the product of squares of vertex degrees, and the second multiplicative Zagreb index $\prod_2(G) $ is the product of products of degrees of pairs of adjacent vertices. In this paper, we explore graphs with extremal $\Pi_{1}(G)$ and $\Pi_{2}(G)$ in terms of (edge) connectivity and pendant vertices. The corresponding extremal graphs are characterized with given connectivity at most $k$ and $p$ pendant vertices. In addition, the maximum and minimum values of $\prod_1(G) $ and $\prod_2(G) $ are provided. Our results extend and enrich some known conclusions. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://export.arxiv.org/pdf/1711.09014 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1711.09014v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
