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2018•Unpublished venueRequires access

CHROMATIC NUMBER TO THE TRANSFORMATION (G---) OF K(1,n) AND K(m,n)

B. Stephen John

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Abstract

Let  be an undirected simple graph. The transformation graph  ofG is a simple graph with vertex set  in which adjacency is defined as follows: (a) two elements in  are adjacent if and only if they are non-adjacent in  (b) two elements in  are adjacent if and only if they are non-adjacent in  and (c) an element of   and an element of   are adjacent if and only if they are non-incident in .In this paper, we determine the chromatic number of Transformation graph  for Star and Complete Bipartite graph. Keywords : Star Graph, Complete Bipartite Graph, Chromatic Number, Transformation Graph

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What this paper is about

Let  be an undirected simple graph. The transformation graph  ofG is a simple graph with vertex set  in which adjacency is defined as follows: (a) two elements in  are adjacent if and only if they are non-adjacent in  (b) two elements in  are adjacent if and only if they are non-adjacent in  and (c) an element of   and an element of   are adjacent if and only if they are non-incident in .In this paper, we determine the chromatic number of Transformation graph  for Star and Complete Bipartite graph. Keywords : Star Graph, Complete Bipartite Graph, Chromatic Number, Transformation Graph

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Available abstract

Let  be an undirected simple graph. The transformation graph  ofG is a simple graph with vertex set  in which adjacency is defined as follows: (a) two elements in  are adjacent if and only if they are non-adjacent in  (b) two elements in  are adjacent if and only if they are non-adjacent in  and (c) an element of   and an element of   are adjacent if and only if they are non-incident in .In this paper, we determine the chromatic number of Transformation graph  for Star and Complete Bipartite graph. Keywords : Star Graph, Complete Bipartite Graph, Chromatic Number, Transformation Graph

Key concepts: Windmill graph, Combinatorics, Mathematics, Butterfly graph, Foster graph, Edge-transitive graph, Friendship graph, Voltage graph

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CHROMATIC NUMBER TO THE TRANSFORMATION (G---) OF K(1,n) AND K(m,n) — Research Paper | ScholarLens