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2023•Advances and Applications in Discrete MathematicsOpen access

RESULTS ON GRUNDY CHROMATIC NUMBER OF JOIN GRAPH OF GRAPHS

R. Stella Maragatham, Arunkumar Subramanian

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Abstract

The Grundy number of a graph G, denoted by $\Gamma(G)$ is the largest k such that G has a greedy k-coloring, that is a coloring with k colors obtained by applying the greedy algorithm according to some ordering of the vertices of G. In this paper, we obtain the Grundy chromatic number of join graph of path graph, complete bipartite graph, fan graph, cycle graph, complete graph, wheel graph and gear graph. Received: February 11, 2023 Revised: May 16, 2023 Accepted: June 6, 2023

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The Grundy number of a graph G, denoted by $\Gamma(G)$ is the largest k such that G has a greedy k-coloring, that is a coloring with k colors obtained by applying the greedy algorithm according to some ordering of the vertices of G. In this paper, we obtain the Grundy chromatic number of join graph of path graph, complete bipartite graph, fan graph, cycle graph, complete graph, wheel graph and gear graph. Received: February 11, 2023 Revised: May 16, 2023 Accepted: June 6, 2023

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Available abstract

The Grundy number of a graph G, denoted by $\Gamma(G)$ is the largest k such that G has a greedy k-coloring, that is a coloring with k colors obtained by applying the greedy algorithm according to some ordering of the vertices of G. In this paper, we obtain the Grundy chromatic number of join graph of path graph, complete bipartite graph, fan graph, cycle graph, complete graph, wheel graph and gear graph. Received: February 11, 2023 Revised: May 16, 2023 Accepted: June 6, 2023

Key concepts: Combinatorics, Windmill graph, Butterfly graph, Graph power, Simplex graph, Wheel graph, Mathematics, Voltage graph

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