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- W4286957066 abstract "Let $G=(V,E)$ be a finite simple graph. The Graovac-Ghorbani index of a graph G is defined as $ABC_{GG}(G)=sum_{uvin E(G)}sqrt{frac{n_u(uv,G)+n_v(uv,G)-2}{n_u(uv,G)n_v(uv,G)}},$ where $n_u(uv,G)$ is the number of vertices closer to vertex $u$ than vertex $v$ of the edge $uvin E(G)$. $n_v(uv,G)$ is defined analogously. The atom-bond connectivity index of a graph G is defined as $ABC(G)=sum_{uvin E(G)}sqrt{frac{d_u+d_v-2}{d_ud_v}},$ where $d_u$ is the degree of vertex $u$ in $G$. Let $G$ be a connected graph constructed from pairwise disjoint connected graphs $G_1,ldots ,G_k$ by selecting a vertex of $G_1$, a vertex of $G_2$, and identifying these two vertices. Then continue in this manner inductively. We say that $G$ is obtained by point-attaching from $G_1, ldots ,G_k$ and that $G_i$'s are the primary subgraphs of $G$. In this paper, we give some lower and upper bounds on Graovac-Ghorbani and atom-bond connectivity indices for these graphs. Additionally, we consider some particular cases of these graphs that are of importance in chemistry and study their Graovac-Ghorbani and atom-bond connectivity indices." @default.
- W4286957066 created "2022-07-25" @default.
- W4286957066 creator A5046055715 @default.
- W4286957066 date "2021-09-28" @default.
- W4286957066 modified "2023-09-29" @default.
- W4286957066 title "On the Graovac-Ghorbani and atom-bond connectivity indices of graphs from primary subgraphs" @default.
- W4286957066 doi "https://doi.org/10.48550/arxiv.2109.13564" @default.
- W4286957066 hasPublicationYear "2021" @default.
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