On the set chromatic number of the join and comb product of graphs
A vertex coloring c : V(G) → of a non-trivial connected graph G is called a set coloring if NC(u) ≠ NC(v) for any pair of adjacent vertices u and v. Here, NC(x) denotes the set of colors assigned to vertices adjacent to x. The set chromatic number of G, denoted by χs (G), is defined as the fewest n...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | text |
| Published: |
Archīum Ateneo
2020
|
| Subjects: | |
| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/124 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1123&context=mathematics-faculty-pubs |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Ateneo De Manila University |
| Summary: | A vertex coloring c : V(G) → of a non-trivial connected graph G is called a set coloring if NC(u) ≠ NC(v) for any pair of adjacent vertices u and v. Here, NC(x) denotes the set of colors assigned to vertices adjacent to x. The set chromatic number of G, denoted by χs (G), is defined as the fewest number of colors needed to construct a set coloring of G. In this paper, we study the set chromatic number in relation to two graph operations: join and comb prdocut. We determine the set chromatic number of wheels and the join of a bipartite graph and a cycle, the join of two cycles, the join of a complete graph and a bipartite graph, and the join of two bipartite graphs. Moreover, we determine the set chromatic number of the comb product of a complete graph with paths, cycles, and large star graphs. |
|---|