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- Title
On the Semitotal Forcing Number of a Graph.
- Authors
Chen, Qin
- Abstract
Zero forcing is an iterative graph coloring process that starts with a subset S of "colored" vertices, all other vertices being "uncolored". At each step, a colored vertex with a unique uncolored neighbor forces that neighbor to be colored. If at the end of the forcing process all the vertices of the graph are colored, then the initial set S is called a zero forcing set. If in addition, every vertex in S is within distance 2 of another vertex of S, then S is a semitotal forcing set. The semitotal forcing number F t 2 (G) of a graph G is the cardinality of the smallest semitotal forcing set of G. In this paper, we begin to study basic properties of F t 2 (G) , relate F t 2 (G) to other domination parameters, and establish bounds on the effects of edge operations on the semitotal forcing number. We also investigate the semitotal forcing number for subfamilies of cubic graphs.
- Subjects
DOMINATING set; GRAPH coloring; PETERSEN graphs
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2022, Vol 45, Issue 3, p1409
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-021-01236-2