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pro vyhledávání: '"Dankelmann Peter"'
Autor:
Dankelmann, Peter
In this paper we obtain bounds on a very general class of distance-based topological indices of graphs, which includes the Wiener index, defined as the sum of the distances between all pairs of vertices of the graph, and most generalisations of the W
Externí odkaz:
http://arxiv.org/abs/2411.13439
Autor:
Balbuena, Camino, Dankelmann, Peter
Let $G$ be a connected graph. The edge-connectivity of $G$, denoted by $\lambda(G)$, is the minimum number of edges whose removal renders $G$ disconnected. Let $\delta(G)$ be the minimum degree of $G$. It is well-known that $\lambda(G) \leq \delta(G)
Externí odkaz:
http://arxiv.org/abs/2408.09020
Let $G$ be a finite, simple connected graph. The average distance of a vertex $v$ of $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The remoteness $\rho(G)$ of $G$ is the maximum of the average distances of the ver
Externí odkaz:
http://arxiv.org/abs/2405.15058
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 37, Iss 3, Pp 823-834 (2017)
For positive integers Δ and D we define nΔ,D to be the largest number of vertices in an outerplanar graph of given maximum degree Δ and diameter D. We prove that nΔ,D=ΔD2+O (ΔD2−1)$n_{\Delta ,D} = \Delta ^{{D \over 2}} + O\left( {\Delta ^{{D
Externí odkaz:
https://doaj.org/article/58f66e343f9c410e89e7f50fdbbeb213
Autor:
Dankelmann, Peter
The Wiener index of a strong digraph $D$ is defined as the sum of the distances between all ordered pairs of vertices. This definition has been extended to digraphs that are not necessarily strong by defining the distance from a vertex $a$ to a verte
Externí odkaz:
http://arxiv.org/abs/2209.08946
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 24, no 2, Graph Theory (November 30, 2022) dmtcs:9432
The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the maximum of the average dis
Externí odkaz:
http://arxiv.org/abs/2201.09269
Autor:
Dankelmann, Peter, Mafunda, Sonwabile
The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the maximum of the average dis
Externí odkaz:
http://arxiv.org/abs/2106.02500
Autor:
Dankelmann, Peter
The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. A connected graph is Eulerian if its vertex degrees are all even. In [Gutman, Cruz, Rada, Wiener index of Eulerian Graphs, Discrete Applied Mat
Externí odkaz:
http://arxiv.org/abs/2101.08342
Autor:
Dankelmann, Peter, Alochukwu, Alex
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 23 no. 1, Graph Theory (June 3, 2021) dmtcs:6956
Let $G$ be a connected graph of order $n$.The Wiener index $W(G)$ of $G$ is the sum of the distances between all unordered pairs of vertices of $G$. In this paper we show that the well-known upper bound $\big( \frac{n}{\delta+1}+2\big) {n \choose 2}$
Externí odkaz:
http://arxiv.org/abs/2011.13970
The eccentric sequence of a connected graph $G$ is the nondecreasing sequence of the eccentricities of its vertices. The Wiener index of $G$ is the sum of the distances between all unordered pairs of vertices of $G$. The unique trees that minimise th
Externí odkaz:
http://arxiv.org/abs/2005.09462