Connectivity of the mycielskian of a graph
WebMay 15, 2024 · The Mycielskian construction, denoted μ ( G ), takes a finite simple graph G to a larger graph with of the same clique number but larger chromatic number. The generalized Mycielskian construction, denoted μ t ( G ), takes G to a larger graph with the same chromatic number but with larger odd girth. WebApr 19, 2024 · The line Mycielskian graph of a graph G, denoted by L µ (G), is the graph obtained from L (G) by adding q + 1 new vertices E = {e i : 1 ≤ i ≤ q} and e, then for 1 ≤ i ≤ q, joining e i to...
Connectivity of the mycielskian of a graph
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WebNov 1, 2024 · In this paper we use the classical notion of weak Mycielskian M′ (G) of a graph G and the following sequence: M′0 (G) = G, M′1 (G) = M′ (G), and M′n (G) = M′ (M′n−1 (G)), to show ... WebApr 15, 2024 · In this section, we study the generalized 3-connectivity of the Mycielskian of any graph and obtain the following result. Theorem 3.1 If G is a connected graph with n ≥ 3 vertices and μ ( G) is the Mycielskian of G, then κ 3 ( μ ( G)) ≥ κ 3 ( G) + 1. Proof Note that κ 3 ( μ ( G)) = min { κ ( S) S ⊆ V ( μ ( G)) a n d S = 3 }.
WebMar 29, 2012 · This paper investigates the vertex-connectivity κ and arc-connectivity κ′ of the generalised Mycielskian of strongly connected digraphs D. We show that κ (μ m (D)) … WebNov 25, 2024 · The Mycielski construction gives us a sequence of graphs that have an arbitrarily high chromatic number for a different reason. In fact, their clique number stays at 2: the Mycielski graphs don't even contain any triangles! Such graphs are hard to come up with by hand, so they're a good source of examples and counter-examples.
WebAll graphs considered in this paper are simple, finite, nontrivial and undirected. Let G be a graph with vertex set \(V^0=\{v_0^0,v_1^0,\ldots,v_{n-1}^0\}\) and edge set E 0.Given an integer m ≥ 1, the m-Mycielskian (also known as the generalized Mycielskian) of G, denoted by μ m (G), is the graph whose vertex set is the disjoint union WebOct 1, 2009 · Generalized Mycielskian of a graph is the natural generalization of the Mycielskian of a graph, which preserves some nice properties of a good …
WebFeb 25, 2011 · Mycielski introduced a new graph transformation μ ( G) for graph G, which is called the Mycielskian of G. A graph G is super connected or simply super- κ (resp. …
WebApr 1, 2016 · On secure domination number of generalized Mycielskian of some graphs. P. G. Nayana, R. R. Iyer. Mathematics. Journal of Intelligent & Fuzzy Systems. 2024. Generalized Mycielskians are triangle-free networks with a large chromatic number, having a number of desirable characteristics like fast multi-path communication, high fault … ovaltine bottleWebJul 1, 2013 · Generalized Mycielskian of a graph is the natural generalization of the Mycielskian of a graph, which preserves some nice properties of a good interconnection network. ... S.F. Raj, Connectivity ... rakhi starts from point qWebThe Mycielskian graph sequence generates graphs that are triangle-free and with a known chromatic number (i.e. the minimum number of colors required to color the vertices of the graph). The sequence starts with a 2 vertex, 1 edge graph (denoted M2) and repeatedly generates subsequent graphs by applying the Mycielskian operation. ... ovaltine and waterWebIn this direction, we prove that the Mycielskian of the bipartite graphs, complete multipartite graphs, {P 5, K 3}-free graphs, {P 5, K 4, K i t e, B u l l} ... Balakrishnan and S. F. Raj, Connectivity of the Mycielskian of a graph, Discrete Math. 308 (2008) 2607–2610. Google Scholar; rakhi send to new zealandWebJun 28, 2008 · The connectivity of a connected graph G is the least positive integer k such that there exists and ⧹ is disconnected or reduces to the trivial graph . An … rakhi set of 5WebIn the following theorem, we determine vertex–connectivity of line Mycielskian graph (L (G)) and the edge–connectivity of line Mycielskian graph h(L (G)) of a graph. … rakhi shoe \u0026 sweater ltdWebApr 15, 2024 · In this section, we study the generalized 3-connectivity of the Mycielskian of any graph and obtain the following result. Theorem 3.1 If G is a connected graph with n ≥ 3 vertices and μ ( G) is the Mycielskian of G, then κ 3 ( μ ( G)) ≥ κ 3 ( G) + 1. Proof Note that κ 3 ( μ ( G)) = min { κ ( S) S ⊆ V ( μ ( G)) a n d S = 3 }. rakhisi hesyre was a dentist for