Harmonious colouring of line graph of commuting and non-commuting graph of D_{2n}
Abstract
Harmonious coloring of graph \(G\) is a proper vertex coloring, where each pair of colors occurs at most on one pair of adjacent vertices. Minimum number of colors required for Harmonious coloring of \(G\) is the harmonious chromatic number, \(\chi_{H}(G)\). Here we determine the Harmonious chromatic number of the line graph of commuting graph and non-commuting graph of the dihedral group, \(D_{2n}\).
2020 Mathematics Subject Classification:
05C25, 05C76Keywords
harmonious coloring, harmonious chromatic number, Dihedral group, line graph
Author Details
R. Divya
Department of Mathematics
Sri Parasakthi College for Women, Courtallam
Affiliated to Manonmaniam Sundaranar University
Tirunelveli – 627 012, Tamil Nadu, India
e-mail: divyaramakrishnan1224@gmail.com
P. Chithra Devi
Department of Mathematics
Sri Parasakthi College for Women, Courtallam
Affiliated to Manonmaniam Sundaranar University
Tirunelveli – 627 012, Tamil Nadu, India
e-mail: chithradevi095@gmail.com
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