
1by Beineke, Lowell W Wilson, Robin J Oellermann, Ortrud R“...No other book covers such a wide scope of this aspect of graph theory...”
edited by Beineke, Lowell W. ¬[Hrsg.]
2013

2“...This article focuses on properties and structures of trees with maximum mean subtree order in a given family; such trees are called optimal in the family. Our...”

3by Casablanca, Rocío M Mol, Lucas Oellermann, Ortrud R Published in Discrete Applied Mathematics (31.01.2021)“...Let G be a (multi)graph of order n and let u,v be vertices of G. The maximum number of internally disjoint u–v paths in G is denoted by κG(u,v), and the...”

4by Mol, Lucas Murphy, Matthew J.H Oellermann, Ortrud R Published in Discrete Applied Mathematics (15.12.2020)“...Let G be a graph, and let u, v, and w be vertices of G. If the distance between u and w does not equal the distance between v and w, then w is said to resolveu...”

5by Moravcik, Gaia Oellermann, Ortrud R Yusim, Samuel Published in Discrete Applied Mathematics (01.03.2017)“...Byline: Gaia Moravcik (a), Ortrud R. Oellermann (a), Samuel Yusim (b) Let G be a graph and u,v be any two distinct vertices of G. A vertex w of G resolves u...”

6“...This article focuses on the problem of determining the mean orders of sub‐k‐trees of k‐trees. It is shown that the problem of finding the mean order of all...”

7by Lafrance, Philip Oellermann, Ortrud R Pressey, Timothy Published in Discrete Applied Mathematics (10.01.2017)“...Suppose V is a finite set and C a collection of subsets of V that contains 0̸ and V and is closed under taking intersections. Then C is called a convexity and...”

8“...Let G be a graph with vertex set V(G). A set C of vertices of G is gconvex if for every pair $${u, v \in C}$$ u , v ∈ C the vertices on every u–v geodesic...”

9by Borchert, Adam Nicol, Skylar Oellermann, Ortrud R Published in Quaestiones mathematicae (15.12.2016)“...Let be a graph property. A graph G is said to be locally (closed locally ) if the subgraph induced by the open neighbourhood (closed neighbourhood,...”

10by Nielsen, Morten H Oellermann, Ortrud R Published in SIAM journal on discrete mathematics (01.01.2009)“...Let $V$ be a finite set and $\mathcal{M}$ a collection of subsets of $V$. Then $\mathcal{M}$ is an alignment of $V$ if and only if $\mathcal{M}$ is closed...”

11by Fehr, Melodie Gosselin, Shonda Oellermann, Ortrud R Published in Aequationes mathematicae (01.03.2006)“...Let G be a (di)graph and S a set of vertices of G. We say S resolves two vertices u and v of G if d(u, S) ≠ d(v, S). A partition $$ \prod $$ = {P1, P2,..., Pk}...”

12by Borchert, Adam Nicol, Skylar Oellermann, Ortrud R Published in Discrete Applied Mathematics (31.05.2016)“...Let P be a graph property. A graph G is said to be locallyP if the subgraph induced by the open neighbourhood of every vertex in G has property P. Ryjáček’s...”

13“...The Wiener polynomial of a connected graph G is defined as W(G;x)=∑xd(u,v), where d(u,v) denotes the distance between u and v, and the sum is taken over all...”

14by Benakli, Nadia Bong, Novi H Dueck, Shonda Eroh, Linda Novick, Beth Oellermann, Ortrud R Published in Discrete mathematics (01.07.2021)“...Let G be a connected graph and u,v and w vertices of G. Then w is said to strongly resolveu and v, if there is either a shortest uw path that contains v or a...”

15“...Let G be a connected (di)graph. A vertex w is said to strongly resolve a pair u , v of vertices of G if there exists some shortest u – w path containing v or...”

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17“...A subset S of vertices of a graph G is gconvex if whenever u and v belong to S, all vertices on shortest paths between u and v also lie in S. The gspectrum...”

18by RodríguezVelázquez, Juan A Yero, Ismael G Kuziak, Dorota Oellermann, Ortrud R Published in Discrete mathematics (28.11.2014)“...Let G be a connected graph. A vertex wstrongly resolves a pair u,v of vertices of G if there exists some shortest u−w path containing v or some shortest v−w...”

19by Lafrance, Philip Oellermann, Ortrud R Pressey, Timothy Published in Graphs and combinatorics (01.03.2016)“...A set S of vertices in a graph G with vertex set V is digitally convex if for every vertex $$v \in V$$ v ∈ V , $$N[v] \subseteq N[S]$$ N [ v ] ⊆ N [ S ]...”

20by van Aardt, Susan A Frick, Marietjie Oellermann, Ortrud R de Wet, Johan Published in Discrete Applied Mathematics (31.05.2016)“...Let P be a graph property. A graph G is said to be locallyP if the subgraph induced by the open neighbourhood of every vertex in G has property P. Ryjáček’s...”