Abstract
A Star coloring of an undirected graph G is a proper vertex coloring of G in which every path on four vertices contains at least three distinct colors. The Star chromatic number of an undirected graph Χs(G), denoted by(G) is the smallest integer k for which G admits a star coloring with k colors. In this paper, we obtain the exact value of the Star chromatic number of Middle graph of Tadpole graph, Snake graph, Ladder graph and Sunlet graphs denoted by M(Tm,n), M(Tn),M(Ln) and M(Sn) respectively.
Highlights
AND PRELIMINARIESThroughout this paper we consider the graph G = (V,E) as a undirected, simple, finite and connected graph with no loops
A proper vertex coloring of a graph is said to be star coloring if the induced subgraph of any two color classes is a collection of stars
In 1973, Branko Grünbaum (5) introduced the concept of star coloring and he introduce the notion of star chromatic number
Summary
A proper vertex coloring of a graph is said to be star coloring if the induced subgraph of any two color classes is a collection of stars. In 1973, Branko Grünbaum (5) introduced the concept of star coloring and he introduce the notion of star chromatic number In the beginning, he developed a new concept called acyclic coloring, where it is required that every cycle uses at least 3 colors, so the 2 color induced subgraphs are Forests. Any hypercube edge joining snake vertices is a snake edge It is denoted by Tn. The Ladder graph (7) is a planar undirected graph with 2n vertices and 3n-2 edges. By the definition of Middle graph, subdividing each edge of Tm,n exactly once and joining all the new vertices of adjacent edges of Tm,n.
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