نتایج جستجو برای: mycielski graph

تعداد نتایج: 198092  

Journal: :Discussiones Mathematicae Graph Theory 2013
R. Pandiyaraj H. P. Patil

The technique of counting cliques in networks is a natural problem. In this paper, we develop certain results on counting of triangles for the total graph of the Mycielski graph or central graph of star as well as completegraph families. Moreover, we discuss the upper bounds for the number of triangles in the Mycielski and other well known transformations of graphs. Finally, it is shown that th...

2015
SHENGJIE HE Liancui Zuo

A linear k-forest of an undirected graph G is a subgraph of G whose components are paths with lengths at most k. The linear k-arboricity Of G, denoted by lak(G), is the minimum number of linear k-forests needed to partition the edge set E(G) of G. In case that the lengths of paths are not restricted, we then have the linear arboricity ofG, denoted by la(G). In this paper, the exact values of th...

Journal: :Discrete Applied Mathematics 2006
Wensong Lin Jianzhuan Wu Peter Che Bor Lam Guohua Gu

The generalized Mycielskians (also known as cones over graphs) are the natural generalization of the Mycielski graphs (which were first introduced by Mycielski in 1955). Given a graph G and any integer m 0, one can transform G into a new graph m(G), the generalized Mycielskian of G. This paper investigates circular clique number, total domination number, open packing number, fractional open pac...

Journal: :Discussiones Mathematicae Graph Theory 2015
S. F. Forouhandeh Nader Jafari Rad R. Pandiyaraj H. P. Patil B. Vaqari Motlagh

Erratum: Identification and corrections of the existing mistakes in the paper On the total graph of Mycielski graphs, central graphs and their covering numbers, Discuss. Math. Graph Theory 33 (2013) 361–371.

2017
Nilanjan De

The generalized Mycielskians are the generalization of the Mycielski graphs, which were introduced by Mycielski in 1955. A topological index is a numeric parameter mathematically derived from a graph and is invariant under automorphism of graphs. Topological indices are widely used for establishing correlations between the structure of a molecular compound and its different physico-chemical pro...

2016
Nilanjan De

The Narumi-Katayama index of a graph G is equal to the product of degrees of all the vertices of G. In this paper, we examine the NarumiKatayama index of some derived graphs such as a Mycielski graph, subdivision graphs, double graph, extended double cover graph, thorn graph, subdivision vertex join and edge join graphs.

Journal: :Asian research journal of mathematics 2023

For a nontrivial connected graph G, non-empty set S \(\subseteq\) V (G) is bipartite dominating of if the subgraph G[S] induced by and for every vertex not in dominated any S. The domination number denoted \(\gamma\)bip(G) G minimum cardinality G. In this paper, we determine exact crown its mycielski as well path cycle graphs.

2010
Tim Meagher

We consider a number of related results taken from two papers – one by W. Lin [1], and the other D. C. Fisher[2]. These articles treat various forms of graph colorings and the famous Mycielski construction. Recall that the Mycielskian μ(G) of a simple graph G is a graph whose chromatic number satisfies χ(μ(G)) = χ(G)+1, but whose largest clique is no larger than the largest clique in G. Extendi...

2009
Zuqiang Ma Junliang Cai

As a natural generalization of chromatic number of a graph, the circular chromatic number of graphs (or the star chromatic number) was introduced by A.Vince in 1988. Let M (G) denote the tth iterated Mycielski graph of G. It was conjectured by Chang, Huang and Zhu(Discrete mathematics,205(1999), 23-37) that for all n ≥ t+2, χc(M (Kn)) = χ(M (Kn)) = n+ t. In 2004, D.D.F. Liu proved the conjectur...

2012
GORD SIMONS CLAUDE TARDIF DAVID WEHLAU

We prove that the coindex of the box complex B(H) of a graph H can be measured by the generalised Mycielski graphs which admit a homomorphism to it. As a consequence, we exhibit for every graph H a system of linear equations solvable in polynomial time, with the following properties: If the system has no solutions, then coind(B(H)) + 2 ≤ 3; if the system has solutions, then χ(H) ≥ 4.

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