# Fall coloring of graphs I

@article{Balakrishnan2010FallCO, title={Fall coloring of graphs I}, author={Rangaswami Balakrishnan and T. Kavaskar}, journal={Discuss. Math. Graph Theory}, year={2010}, volume={30}, pages={385-391} }

A fall coloring of a graph G is a proper coloring of the vertex set of G such that every vertex of G is a color dominating vertex in G (that is, it has at least one neighbor in each of the other color classes). The fall coloring number f(G) of G is the minimum size of a fall color partition of G (when it exists). Trivially, for any graph G, (G) f(G). In this paper, we show the existence of an innite family of graphs G with prescribed values for (G) and f(G). We also obtain the smallest non-fall…

## 7 Citations

### Fall coloring and b-coloring of graphs

- MathematicsJournal of Physics: Conference Series
- 2018

The b-chromatic number of G, denoted by φ(G), is the maximum k for which G has a b-coloring by k colors. A b-coloring of G by k colors is a proper k-coloring of the vertices of G such that in each…

### Algorithmic aspects of graph colourings heuristics

- Mathematics
- 2012

A proper colouring of a graph is a function that assigns a colour to each vertex with the restriction that adjacent vertices are assigned with distinct colours. Proper colourings are a natural model…

### Color Chain of a Graph

- MathematicsGraphs Comb.
- 2011

This paper exhibits an infinite family of graphs G with a strictly increasing color chain: $$chi (G) < \chi_f(G) = \Psi_f (G), \phi(G), < \partial \Gamma (G%) < \PsI (G)}$$ .

### The energy of the Mycielskian of a regular graph

- MathematicsAustralas. J Comb.
- 2012

The energy of the Mycielskian of a connected regular graph G is determined in terms of the energy E(G) of G, where the energy of G is the sum of the absolute values of the eigenvalues of G.

### Algorithmic aspects of graph colouring heuristics

- Mathematics
- 2012

Une coloration propre d’un graphe est une fonction qui attribue une couleur a chaque sommet du graphe avec la restriction que deux sommets voisins ont des couleurs distinctes. Les colorations…

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