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On the basis number and the minimum cycle bases of the wreath product of some graphs II
(
University of Zielona Gora
, 2010 , Article)
A construction of a minimum cycle bases for the wreath product of a star by a path, two stars and a star by a wheel is given. Moreover, the basis numbers of these products are determined.
Minimum cycle bases for direct products of K2 with complete graphs
(
University of Queensland Press
, 2009 , Article)
We construct a minimum cycle basis for the direct product K2 x Kp of two complete graphs where p > 2. For p > 3, these bases consists only of squares. This completes the work of R. Hammack, who treated the case Kp x ...
On the basis number of the wreath product of paths with wheels and some related problems
(
Charles Babbage Research Centre
, 2017 , Article)
In this paper, we investigate the basis number for the wreath product of wheels with paths. Also, as a related problem, we construct a minimum cycle basis of the same.
A new upper bound of the basis number of the lexicographic product of graphs
(
Charles Babbage Research Centre
, 2010 , Article)
An upper bound of the basis number of the lexicographic product of two graphs from the basis number of the factors is presented. Furthermore, the basis numbers of the lexicographic product of some classes of graphs is determined.
Edge-Maximal Graphs Without θ2k+1-Graphs
(
Taylor and Francis Ltd.
, 2014 , Article)
Let σ(n; θ2k+1) denote the class of non-bipartite graphs on n vertices having no θ2k+1- graph and f(n; θ2k+1) = max{ ε(G): G ∊ σ (n; θ2k+1)}. In this paper we determine f(n; θ2k+1), by proving that for k ≥ 4 and n ≥ 36k. ...
Edge Maximal C2k+1-edge Disjoint Free Graphs
(
University of Zielona Gora
, 2012 , Article)
For two positive integers r and s, G(n;r,s) denotes to the class of graphs on n vertices containing no r of s-edge disjoint cycles and f(n;r,s) = max{E(G):G ∈ G(n;r,s)}. In this paper, for integers r ≥ 2 and k ≥ 1, we ...
Edge-maximal graphs without θ 7 -graphs
(
Tokyo University of Science
, 2011 , Article)
Let G(n; θ2k+1, ≥ δ) denote the class of non-bipartite θ2k+1-free graphs on n vertices and minimum degree at least δ and let f (n; θ2k+1, ≥ δ) = max{ε(G): G ∈ G(n; θ2k+1, ≥ δ)}. In this paper we determinj an upker bound ...
On minimum cycle bases of the wreath product of wheels with stars
(
Zenodo
, 2010 , Article)
The length of a cycle basis of a graph is the sum of the lengths of its elements. A minimum cycle basis is a cycle basis with minimum length. In this work, a construction of a minimum cycle basis for the wreath product of ...
Fundamental group and cycle space of dual graphs and applications
(
Elsevier
, 2010 , Article)
In this work, we study the fundamental group of dual graph of a planar graph. Moreover, we show that a planar graph G has no cut vertex if and only if N(Π(D(G))) = N(Π(D(G − v))) − 1 for any v ∈ V(G). Some applications ...
New solitary wave and computational solitons for Kundu-Eckhaus equation
(
Elsevier
, 2022 , Article)
The goal of this research is to find novel optical solutions to the Kundu-Eckhaus equation, which possess crucial roles in the field of nonlinear optics. A collective variable (CV) strategy is adopted to solve governing ...