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pro vyhledávání: '"Dimitrov, Darko"'
The $\sigma_{t}$-irregularity (or sigma total index) is a graph invariant which is defined as $\sigma_{t}(G)=\sum_{\{u,v\}\subseteq V(G)}(d(u)-d(v))^{2},$ where $d(z)$ denotes the degree of $z$. This irregularity measure was proposed by R\' {e}ti [Ap
Externí odkaz:
http://arxiv.org/abs/2411.04881
The total $\sigma$-irregularity is given by $ \sigma_t(G) = \sum_{\{u,v\} \subseteq V(G)} \left(d_G(u) - d_G(v)\right)^2, $ where $d_G(z)$ indicates the degree of a vertex $z$ within the graph $G$. It is known that the graphs maximizing $\sigma_{t}$-
Externí odkaz:
http://arxiv.org/abs/2411.01530
Autor:
Dimitrov, Darko, Du, Zhibin
The problem of characterizing trees with minimal atom-bond-connectivity index (minimal-ABC trees) has a reputation as one of the most demanding recent open optimization problems in mathematical chemistry. Here firstly, we give an affirmative answer t
Externí odkaz:
http://arxiv.org/abs/2110.14712
Publikováno v:
In Applied Mathematics and Computation 1 April 2025 490
Publikováno v:
Open Mathematics, Vol 21, Iss 1, Pp 63-77 (2023)
The Collatz-Sinogowitz irregularity index is the oldest known numerical measure of graph irregularity. For a simple and connected graph GG of order nn and size mm, it is defined as CS(G)=λ1−2m/n,\hspace{0.1em}\text{CS}\hspace{0.1em}\left(G)={\lamb
Externí odkaz:
https://doaj.org/article/21d7ffcb58584cdfb4bf6c679ac1378a
Autor:
Dimitrov, Darko, Du, Zhibin
Publikováno v:
In Discrete Applied Mathematics 15 September 2023 336:148-194
Autor:
Dimitrov, Darko, Stevanović, Dragan
Publikováno v:
In Applied Mathematics and Computation 15 March 2023 441
Autor:
Ali, Akbar, Dimitrov, Darko
Publikováno v:
Discrete Appl. Math. 238, (2018) 32-40
Many existing degree based topological indices can be classified as bond incident degree (BID) indices, whose general form is $BID(G)=\sum_{uv\in E(G)}$ $\Psi(d_{u},d_{v})$, where $uv$ is the edge connecting the vertices $u,v$ of the graph $G$, $E(G)
Externí odkaz:
http://arxiv.org/abs/1707.00733
Publikováno v:
Applied Mathematics and Computation, Volume 313, 15 November 2017, Pages 418 - 430
The atom-bond connectivity (ABC) index has been, in recent years, one of the most actively studied vertex-degree-based graph invariants in chemical graph theory. For a given graph $G$, the ABC index is defined as $\sum_{uv\in E}\sqrt{\frac{d(u) +d(v)
Externí odkaz:
http://arxiv.org/abs/1706.08680
Autor:
Dimitrov, Darko
The atom-bond connectivity (ABC) index is one of the most investigated degree-based molecular structure descriptors with a variety of chemical applications. It is known that among all connected graphs, the trees minimize the ABC index. However, a ful
Externí odkaz:
http://arxiv.org/abs/1706.08587