The Unit Bar Visibility Number of a Graph
نویسندگان
چکیده
منابع مشابه
The Unit Bar Visibility Number of a Graph
A t-unit-bar representation of a graph G is an assignment of sets of at most t horizontal unit-length segments in the plane to the vertices of G so that (1) all of the segments are pairwise nonintersecting, and (2) two vertices x and y are adjacent if and only if there is a vertical channel of positive width connecting a segment assigned to x and a segment assigned to y that intersects no other...
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We introduce the notion of uniform number of a graph. The uniform number of a connected graph $G$ is the least cardinality of a nonempty subset $M$ of the vertex set of $G$ for which the function $f_M: M^crightarrow mathcal{P}(X) - {emptyset}$ defined as $f_M(x) = {D(x, y): y in M}$ is a constant function, where $D(x, y)$ is the detour distance between $x$ and $y$ in $G$ and $mathcal{P}(X)$ ...
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A triangulated polygon is a 2-connected maximal outerplanar graph. A unit bar-visibility graph (UBVG for short) is a graph whose vertices can be represented by disjoint, horizontal, unit-length bars in the plane so that two vertices are adjacent if and only if there is a nondegenerate, unobstructed, vertical band of visibility between the corresponding bars. We give combinatorial and geometric ...
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Let $G=(V,E)$ be a simple graph. A set $Dsubseteq V$ is adominating set of $G$ if every vertex in $Vsetminus D$ has atleast one neighbor in $D$. The distance $d_G(u,v)$ between twovertices $u$ and $v$ is the length of a shortest $(u,v)$-path in$G$. An $(u,v)$-path of length $d_G(u,v)$ is called an$(u,v)$-geodesic. A set $Xsubseteq V$ is convex in $G$ ifvertices from all $(a, b)$-geodesics belon...
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ژورنال
عنوان ژورنال: Journal of Graph Algorithms and Applications
سال: 2016
ISSN: 1526-1719
DOI: 10.7155/jgaa.00393