Strong Geodetic Number of Complete Bipartite Graphs, Crown Graphs and Hypercubes
نویسندگان
چکیده
منابع مشابه
META-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کاملMatching graphs of Hypercubes and Complete Bipartite Graphs
Kreweras’ conjecture [1] asserts that every perfect matching of the hypercube Qd can be extended to a Hamiltonian cycle. We [2] proved this conjecture but here we present a simplified proof. The matching graph M(G) of a graph G has a vertex set of all perfect matchings of G, with two vertices being adjacent whenever the union of the corresponding perfect matchings forms a Hamiltonian cycle. We ...
متن کاملThe geodetic number of strong product graphs
For two vertices u and v of a connected graph G, the set IG[u, v] consists of all those vertices lying on u − v geodesics in G. Given a set S of vertices of G, the union of all sets IG[u, v] for u, v ∈ S is denoted by IG[S]. A set S ⊆ V (G) is a geodetic set if IG[S] = V (G) and the minimum cardinality of a geodetic set is its geodetic number g(G) of G. Bounds for the geodetic number of strong ...
متن کاملRouting Numbers of Cycles, Complete Bipartite Graphs, and Hypercubes
The routing number rt(G) of a connected graph G is the minimum integer r so that every permutation of vertices can be routed in r steps by swapping the ends of disjoint edges. In this paper, we study the routing numbers of cycles, complete bipartite graphs, and hypercubes. We prove that rt(Cn) = n − 1 (for n ≥ 3) and for s ≥ t, rt(Ks,t) = 3s 2t + O(1). We also prove n + 1 ≤ rt(Qn) ≤ 2n − 2 for ...
متن کاملCyclic type factorizations of complete bipartite graphs into hypercubes
So far, the smallest complete bipartite graph which was known to have a cyclic type decomposition into cubes Qd of a given dimension d was Kd2d−2,d2d−2. Using binary Hamming codes we prove in this paper that there exists a cyclic type factorization of K2d−1,2d−1 into Qd if and only if d is a power of 2.
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: Bulletin of the Malaysian Mathematical Sciences Society
سال: 2019
ISSN: 0126-6705,2180-4206
DOI: 10.1007/s40840-019-00833-6