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On the Recognition of FanPlanar and Maximal OuterFanPlanar Graphs?
"... Abstract. Fanplanar graphs were recently introduced as a generalization of 1planar graphs. A graph is fanplanar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges incident to a common vertex. A graph is outerfanpla ..."
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if it has a fanplanar embedding in which every vertex is on the outer face. If, in addition, the insertion of an edge destroys its outerfanplanarity, then it is maximal outerfanplanar. In this paper, we present a polynomialtime algorithm to test whether a given graph is maximal outerfanplanar
Properties and Complexity of FanPlanarity?
"... Abstract. In a fanplanar drawing of a graph an edge can cross only edges with a common endvertex. Fanplanar drawings have been recently introduced by Kaufmann and Ueckerdt, who proved that every nvertex fanplanar drawing has at most 5n − 10 edges, and that this bound is tight for n ≥ 20. We ext ..."
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Abstract. In a fanplanar drawing of a graph an edge can cross only edges with a common endvertex. Fanplanar drawings have been recently introduced by Kaufmann and Ueckerdt, who proved that every nvertex fanplanar drawing has at most 5n − 10 edges, and that this bound is tight for n ≥ 20. We
T.: The density of fanplanar graphs
 CoRR abs/1403.6184
"... A topological drawing of a graph is fanplanar if for each edge e the edges crossing e have a common endpoint on the same side of e, and a fanplanar graph is a graph admitting such a drawing. Equivalently, this can be formulated by two forbidden patterns, one of which is the configuration where e i ..."
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Cited by 2 (1 self)
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A topological drawing of a graph is fanplanar if for each edge e the edges crossing e have a common endpoint on the same side of e, and a fanplanar graph is a graph admitting such a drawing. Equivalently, this can be formulated by two forbidden patterns, one of which is the configuration where e
Face Labeling Of Maximal Planar Graphs
, 2011
"... The labeling problem considered in this paper is called facelabeling of the maximal planar or triangular planar graphs in connection with the notion of the consistency. Several triangular planar and maximal planar graphs such as the wheels, the fans etc. are considered. ..."
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The labeling problem considered in this paper is called facelabeling of the maximal planar or triangular planar graphs in connection with the notion of the consistency. Several triangular planar and maximal planar graphs such as the wheels, the fans etc. are considered.
Darkfield hyperlens exploiting a planar fan of tips
"... Metallodielectric superlenses transfer subwavelengthscale information without magnification. The socalled hyperlenses additionally magnify, transferring images into traditional farfield optics. We target hyperlenses based on the“canalization ” phenomenon in an array of wires, modified to form an ..."
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an open fan, also called“endoscope. ” We use an integrated optics design with silicon wires, fed for instance by grating couplers, accessing gold wire fans. This alleviates the need to care for wire length. We explore a regime where we do not only image a nearfield source, but where we image illuminated
MOHAMED ESSALIH,
, 1817
"... In this paper, we give some theoretical results, for the index Wiener�, degree distance � � and the hyperWiener index � � of a graph�, according to � ����(The number of pairs of vertices of � that are at distance), and the diameter of �. We accomplish this by firstly, giving another proof of the in ..."
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of the inequality for the planar graphs with �vertices:���� � � ���� � � �����[6], with � � is a maximal planar graph � � is a planar graph and � � is a path planar graph. Secondly, we will apply the theoretical results for some graphs with diameter equals two, as Fan planar graph � �, Wheel planar graph
On economical set representations of graphs
, 2009
"... In this paper we discuss the bounds of and relations among various kinds of intersection numbers of graphs. Especially, we address extremal graphs with respect to the established bounds. The uniqueness of the minimumsize intersection representations for some graphs is also studied. In the course o ..."
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Cited by 1 (0 self)
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In this paper we discuss the bounds of and relations among various kinds of intersection numbers of graphs. Especially, we address extremal graphs with respect to the established bounds. The uniqueness of the minimumsize intersection representations for some graphs is also studied. In the course
Enumerating rooted biconnected planar graphs . . .
"... A graph is called a triangulated planar graph if it admits a plane embedding in the plane such that all inner faces are triangle. In a rooted triangulated planar graph, a vertex and two edges incident to it are designated as an outer vertex and outer edges, respectively. Two plane embedding of roote ..."
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Cited by 4 (4 self)
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A graph is called a triangulated planar graph if it admits a plane embedding in the plane such that all inner faces are triangle. In a rooted triangulated planar graph, a vertex and two edges incident to it are designated as an outer vertex and outer edges, respectively. Two plane embedding
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