In graph theory, a harmonious coloring is a (proper) vertex coloring in which every pair of colors appears on at most one pair of adjacent vertices. It is the opposite of the complete coloring, which instead requires every color pairing to occur at least once.
Dec 29, 2015 · The harmonious number h(D) of D is the smallest k for which there exists a harmonious k-coloring of D. Therefore, for any digraph D of size m we ...
If no pair (i, i) is assigned, then f is said to be a proper harmonious coloring of D. The minimum t for which D admits a proper harmonious coloring is called ...
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Harmonious colorings of regular digraphs. July 2015. Authors: Suresh M. Hegde at National Institute of Technology Karnataka · Suresh M. Hegde · National ...
Proposition 1.4. The proper harmonious coloring number of a symmetric digraph is same as the proper harmonious coloring number of its underlying graph.
Let D be a directed graph with n vertices and m edges. A function f : V(D) → {1, 2, 3, ..., k} where k ≤ n is said to be harmonious coloring of D if for any ...
A harmonious coloring of any digraph D is an assignment of colors to the vertices of D and the color of an arc is defined to be the ordered pair of colors to ...
In this report we define a new coloring of graphs, namely harmonious coloring of graphs, which arises as an extension of harmonious and graceful numbering ...
Nov 30, 2022 · In this paper, we determine digraphs, arising from the Zykov sum of digraphs, which accept a complete k-coloring with k equals their harmonious ...
A harmonious colouring of a simple undirected graph is a proper vertex colouring such that each pair of colours appears together on at most one edge.