We present some sharp bounds on the general degree distance for multipartite graphs and trees of given order, graphs of given order and chromatic number, graphs of given order and vertex connectivity, and graphs of given order and number of pendant vertices.
📌 3 Key Takeaways
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Objective & Hypothesis:We generalize several topological indices and introduce the general degree distance of a connected graph $G$.
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Key Findings & Data:For $a, b \in \mathbb{R}$, the general degree distance $DD_{a,b} (G) = \sum_{ v \in V(G)} [deg_{G}(v)]^a S^b_{G} (v)$, where $V(G)$ is the vertex set of $G$, $deg_G (v)$ is the degree of a vertex $v$, $S^b_{G} (v) = \sum_{ w \in V(G) \setminus \{ v \} } [d_{G} (v,w) ]^{b}$ and $d_{G} (v,w)$ is the distance between $v$ and $w$ in $G$.
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Conclusion & Impact:We present some sharp bounds on the general degree distance for multipartite graphs and trees of given order, graphs of given order and chromatic number, graphs of given order and vertex connectivity, and graphs of given order and number of pendant vertices.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Degree distance · Chromatic number · Vertex connectivity
Abstract
We generalize several topological indices and introduce the general degree distance of a connected graph $G$. For $a, b \in \mathbb{R}$, the general degree distance $DD_{a,b} (G) = \sum_{ v \in V(G)} [deg_{G}(v)]^a S^b_{G} (v)$, where $V(G)$ is the vertex set of $G$, $deg_G (v)$ is the degree of a vertex $v$, $S^b_{G} (v) = \sum_{ w \in V(G) \setminus \{ v \} } [d_{G} (v,w) ]^{b}$ and $d_{G} (v,w)$ is the distance between $v$ and $w$ in $G$. We present some sharp bounds on the general degree distance for multipartite graphs and trees of given order, graphs of given order and chromatic number, graphs of given order and vertex connectivity, and graphs of given order and number of pendant vertices.
VETRÍK, T. (2021). General degree distance of graphs. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 8 - Sayı: 2, 107–118. https://ajindex.com/articles/861499
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