The crossing numbers of join of some graphs with n isolated vertices
نویسندگان
چکیده
منابع مشابه
Crossing numbers of join of a graph on six vertices with a path and a cycle
The crossing number of a graph G is the minimum number of crossings of its edges among the drawings of G in the plane and is denoted by cr(G). Zarankiewicz conjectured that the crossing number of the complete bipartite graph Km,n equals . This conjecture has been verified by Kleitman for min {m, n} ≤ 6. Using this result, we give the exact values of crossing number of the join of a certain grap...
متن کاملThe 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...
متن کاملThe bondage numbers of graphs with small crossing numbers
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 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...
متن کاملCrossing numbers of imbalanced graphs
The crossing number, cr(G), of a graph G is the least number of crossing points in any drawing of G in the plane. According to the Crossing Lemma of Ajtai, Chvátal, Newborn, Szemerédi [ACNS82] and Leighton [L83], the crossing number of any graph with n vertices and e > 4n edges is at least constant times e/n. Apart from the value of the constant, this bound cannot be improved. We establish some...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2018
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2048