The crossing numbers of several graphs of order eight with paths
نویسندگان
چکیده
منابع مشابه
The crossing numbers of join products of paths with graphs of order four
Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87–97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numb...
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The bondage number b(G) of a nonempty graph G is the cardinality of a smallest edge set whose removal from G results in a graph with domination number greater than the domination number (G) ofG. Kang andYuan proved b(G) 8 for every connected planar graph G. Fischermann, Rautenbach and Volkmann obtained some further results for connected planar graphs. In this paper, we generalize their results ...
متن کاملOn the crossing numbers of Cartesian products of paths with special graphs
There are known exact results of the crossing numbers of the Cartesian product of all graphs of order at most four with paths, cycles and stars. Moreover, for the path Pn of length n, the crossing numbers of Cartesian products G Pn for all connected graphs G on five vertices and for forty graphs G on six vertices are known. In this paper, we extend these results by determining the crossing numb...
متن کاملOn the crossing numbers of Cartesian products with paths
Using a newly introduced operation on graphs and its counterpart on graph drawings, we prove the conjecture of Jendrol’ and Ščerbová from 1982 about the crossing number of the Cartesian product K1,m2Pn. Our approach is applicable to the capped Cartesian products of Pn with any graph containing a dominating vertex.
متن کاملCrossing numbers of random graphs
An order type of the points x1, x2, ..., xn in the plane (with no three colinear) is a list of orientations of all triplet xixjxk, i < j < k. Let X be the set of all order types of the points x1, ..., xn in the plane. For any graph G with vertices v1, ..., vn let lin-crξ(G) denote the number of crossings in the straight line drawing of G, where vi is placed at xi in the plane and x1, ..., xn ha...
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ژورنال
عنوان ژورنال: Mathematical Modelling and Geometry
سال: 2019
ISSN: 2311-1275
DOI: 10.26456/mmg/2019-723