Note on Path-Connectivity of Complete Bipartite Graphs
نویسندگان
چکیده
For a graph [Formula: see text] and set of size at least text], path in is said to be an text]-path if it connects all vertices text]. Two text]-paths are internally disjoint Let denote the maximum number The text]-path-connectivity then defined as minimum where ranges over text]-subsets In [M. Hager, Path-connectivity graphs, Discrete Math. 59 (1986) 53–59], complete bipartite was calculated, But, from his proof, only case that considered. this paper, we calculate situation result.
منابع مشابه
The generalized connectivity of complete bipartite graphs
Let G be a nontrivial connected graph of order n, and k an integer with 2 ≤ k ≤ n. For a set S of k vertices of G, let κ(S) denote the maximum number l of edge-disjoint trees T1, T2, . . . , Tl in G such that V (Ti) ∩ V (Tj) = S for every pair i, j of distinct integers with 1 ≤ i, j ≤ l. Chartrand et al. generalized the concept of connectivity as follows: The k-connectivity, denoted by κk(G), o...
متن کاملMETA-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 کاملNote on the Rainbow $k$-Connectivity of Regular Complete Bipartite Graphs
A path in an edge-colored graph G, where adjacent edges may be colored the same, is called a rainbow path if no two edges of the path are colored the same. For a κ-connected graph G and an integer k with 1 ≤ k ≤ κ, the rainbow kconnectivity rck(G) of G is defined as the minimum integer j for which there exists a j-edge-coloring of G such that any two distinct vertices of G are connected by k in...
متن کاملA Note on Path Factors of (3,4)-Biregular Bipartite Graphs
A proper edge coloring of a graph G with colors 1, 2, 3, . . . is called an interval coloring if the colors on the edges incident with any vertex are consecutive. A bipartite graph is (3, 4)-biregular if all vertices in one part have degree 3 and all vertices in the other part have degree 4. Recently it was proved [J. Graph Theory 61 (2009), 88-97] that if such a graph G has a spanning subgraph...
متن کاملNote on cyclic decompositions of complete bipartite graphs into cubes
So far, the smallest complete bipartite graph which was known to have a cyclic decomposition into cubes Qd of a given dimension d was Kd2d−1,d2d−2 . We improve this result and show that also Kd2d−2,d2d−2 allows a cyclic decomposition into Qd. We also present a cyclic factorization of K8,8 into Q4.
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: Journal of Interconnection Networks
سال: 2021
ISSN: ['0219-2659', '1793-6713']
DOI: https://doi.org/10.1142/s0219265921420147