On r-dynamic Coloring of Ladder Graph and Tadpole Graph Using m-shadow Operation

Authors

  • I. H. Agustin PUI-PT Combinatorics and Graph, CGANT University of Jember, Indonesia
  • A. Irin Feno PG and Research Department of Mathematics, Kongunadu Arts and Science College, Coimbatore-641 029, Tamil Nadu, India
  • K. Abirami PG and Research Department of Mathematics, Kongunadu Arts and Science College, Coimbatore-641 029, Tamil Nadu, India
  • M. Venkatachalam PG and Research Department of Mathematics, Kongunadu Arts and Science College, Coimbatore-641 029, Tamil Nadu, India https://orcid.org/0000-0001-5051-4104
  • Dafik PUI-PT Combinatorics and Graph, CGANT University of Jember, Indonesia
  • N. Mohanapriya PG and Research Department of Mathematics, Kongunadu Arts and Science College, Coimbatore-641 029, Tamil Nadu, India

DOI:

https://doi.org/10.37256/cm.5120242624

Keywords:

r-dynamic coloring, m-shadow graph, ladder graph, tadpole graph

Abstract

An r-dynamic coloring is a proper k-coloring of a graph G = {V,E} such that the neighbors of every vertex vV(G) is colored using ς: V(G) → S(c) where S(c) is a set of colors. The coloring is made in such a way that it satisfies the conditions: (i) For any edge uvE(G), the color of u and color of v are distinct and (ii) The cardinality of coloring the neighbors of any vertex v should be greater than or equal to min{r, d(vG)}, where d(vG) is the degree of the vertex v. In this paper the lower bounds for the r-dynamic coloring of m-shadow graph of ladder graph Dm(Ln) and tadpole graph Dm(Ln,p) are attained. Using the lower bounds the exact solution of r-dynamic chromatic number of the ladder graph Ln and tadpole graph Ln,p by m-shadow operation are obtained.

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Published

2024-02-27

How to Cite

1.
Agustin IH, Feno AI, Abirami K, Venkatachalam M, Dafik, Mohanapriya N. On r-dynamic Coloring of Ladder Graph and Tadpole Graph Using m-shadow Operation. Contemp. Math. [Internet]. 2024 Feb. 27 [cited 2024 May 28];5(1):827-43. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2624