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- W3108974037 abstract "Let G=(V(G), E(G)) be a path or cycle graph. A subset D of V(G) is a dominating set of G if for every u element of V(G)D, there exists v element of D such that uv element of E(G), that is, N[D]=V(G). The domination number of G, denoted by gamma(G), is the smallest cardinality of a dominating set of G. A set D_1 subset of V(G) is a set containing dominating vertices of degree 2, that is, each vertex is internally stable. A set D_2 subset of V(G) is a set containing dominating vertices where one of the element say a element of D_2, and the rest are of degree 2. A set D_3 subset of V(G) is a set containing dominating vertices in which two of the elements say b, c element of D_3, deg(b)=deg(c)=1. This paper developed a new combinatorial formula that determines the number of ways of putting a dominating set in a path and cycle graphs of order n>=1 and n>=3, respectively. Further, a combinatorial function P^1_G(n), P^2_G(n) and P^3_G(n) that determines the probability of getting the set D_1, D_2, and D_3, respectively in graph G of order n were constructed." @default.
- W3108974037 created "2020-12-07" @default.
- W3108974037 creator A5044829287 @default.
- W3108974037 date "2020-11-23" @default.
- W3108974037 modified "2023-09-27" @default.
- W3108974037 title "NEW COUNTING FORMULA FOR DOMINATING SETS IN PATH AND CYCLE GRAPHS" @default.
- W3108974037 doi "https://doi.org/10.14710/jfma.v3i2.9325" @default.
- W3108974037 hasPublicationYear "2020" @default.
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