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pro vyhledávání: '"Eroh, Linda"'
Autor:
Benakli, Nadia, Bong, Novi H, Dueck, Shonda M., Eroh, Linda, Novick, Beth, Oellermann, Ortrud R.
Let $G$ be a connected graph and $u,v$ and $w$ vertices of $G$. Then $w$ is said to {\em strongly resolve} $u$ and $v$, if there is either a shortest $u$-$w$ path that contains $v$ or a shortest $v$-$w$ path that contains $u$. A set $W$ of vertices o
Externí odkaz:
http://arxiv.org/abs/2008.04282
Publikováno v:
Theoret. Comput. Sci., Vol. 806 (2020) pp.53-69
The notion of metric dimension, $dim(G)$, of a graph $G$, as well as a number of variants, is now well studied. In this paper, we begin a local analysis of this notion by introducing $cdim_G(v)$, \emph{the connected metric dimension of $G$ at a verte
Externí odkaz:
http://arxiv.org/abs/1804.08147
Autor:
Benakli, Nadia, Bong, Novi H., Dueck, Shonda, Eroh, Linda, Novick, Beth, Oellermann, Ortrud R.
Publikováno v:
In Discrete Mathematics July 2021 344(7)
Due to the increasing discovery and implementation of networks within all disciplines of life, the study of subgraph connectivity has become increasingly important. Motivated by the idea of community (or sub-graph) detection within a network/graph, w
Externí odkaz:
http://arxiv.org/abs/1505.04300
Publikováno v:
Acta Math. Sin. (Engl. Ser.), Vol. 33, Issue 6 (2017) pp. 731-747
The \emph{metric dimension} $\dim(G)$ of a graph $G$ is the minimum number of vertices such that every vertex of $G$ is uniquely determined by its vector of distances to the chosen vertices. The \emph{zero forcing number} $Z(G)$ of a graph $G$ is the
Externí odkaz:
http://arxiv.org/abs/1408.5943
Publikováno v:
Discrete Math. Algorithms Appl. Vol. 7(1) (2015) 1550002 (10 pages)
The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G) \setminus S$ are colored white) such that $V(G)$ is turned black after finitely many applications of "the colo
Externí odkaz:
http://arxiv.org/abs/1402.1962
Publikováno v:
Math. Bohem. Vol. 139, No.3 (2014) pp. 467-483
Zero forcing number has recently become an interesting graph parameter studied in its own right since its introduction by the "AIM Minimum Rank -- Special Graphs Work Group", whereas metric dimension is a well-known graph parameter. We investigate th
Externí odkaz:
http://arxiv.org/abs/1207.6127
Publikováno v:
Discrete Math. Algorithms Appl. Vol. 5, No. 4 (2013) 1250060
The \emph{metric dimension} of a graph $G$, denoted by $\dim(G)$, is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let $G_1$ and $G_2$ be disjoint copies of a graph $G$ and let $f
Externí odkaz:
http://arxiv.org/abs/1111.5864
Publikováno v:
Discuss. Math. Graph Theory, Vol. 32 (2012) pp. 299-319
Let $G_1$ and $G_2$ be disjoint copies of a graph $G$, and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a \emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$ and the edge set $E=E(G_1) \cup E(G_2) \cup \{uv \mid u
Externí odkaz:
http://arxiv.org/abs/1106.1147