K-Forcing Number of Some Graphs and Their Splitting Graphs

remodkmuar K P¹ , Charles Dominic² , Baby Chacko³

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.3 , pp.121-127, Jun-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.121127

Online published on Jun 30, 2019

Copyright © Premodkmuar K P , Charles Dominic , Baby Chacko . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Amos et al. instigated the idea of k-forcing number of a graph. For a graph G=(V,E) and a subset Fof G, the vertices in F are called initially colored black vertices and the vertices in V(G)-F are called initially non colored black vertices or white vertices. Then the set F is a k-forcing set of a graph G if all vertices in G will become colored black after applying the subsequent color changing rule. Color changing rule: If a black colored vertex is adjacent to atmost k-white vertices, then the white vertices change to be colored black. The cardinality of a smallest k-forcing set is known as the k-forcing number of the graph G and is represented as Z_k (G). This work is intended to investigate the k-forcing number of the splitting graph of a graph in which k≥2.

Key-Words / Index Term :
Zero Forcing Number, K-forcing Number and Splitting Graph

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