## Abstract

Graph colorings are a major area of study in graph theory involving the constrained assignment of labels(colors) to vertices or edges. There are many types of colorings defined. The most common type of coloring is the proper vertex k-coloring which is defined as a vertex coloring from a set of k colors such that no two adjacent vertices share a common color. Our central focus in this paper is a variant of the proper vertex k-coloring problem, termed graceful coloring introduced by Gary Chartrand in 2015 and defined as follows. A graceful kcoloring of a nonempty graph G is a proper vertex coloring c : V (G) [k], where k-2, that induces a proper edge coloring c0 : E(G) [k-1] defined by c0(uv) = |c(u)-c(v)|. In this work we find the graceful chromatic number for some well-known classes of graphs such as Friendship graph, Petersen graph, Cactus graph and others.

Original language | English |
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Pages | 99-102 |

Number of pages | 4 |

Publication status | Published - Jan 1 2019 |

Event | 17th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2019 - Enschede, Netherlands Duration: Jul 1 2019 → Jul 3 2019 |

### Conference

Conference | 17th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2019 |
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Country | Netherlands |

City | Enschede |

Period | 7/1/19 → 7/3/19 |

## ASJC Scopus subject areas

- Control and Optimization
- Discrete Mathematics and Combinatorics