Weak and strong domination on some graphs
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Date
2022
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Abstract
Let G = (V(G), E(G)) be a graph and uv?E. A subset D âV of vertices is a dominating set if every vertex in V-D is adjacent to at least one vertex of D. The domination number is the minimum cardinality of a dominating set. Let u and v be elements of V. Then, u strongly dominates u and v weakly dominates u if (i)uv?E and (ii)deg(u) ?deg(v). A set D â V is a strong (weak) dominating set (sd-set)(wd-set) of G if every vertex in V-D is strongly dominated by at least one vertex in D. The strong (weak) domination number ?s(?w) of G is the minimum cardinality of a sd-set (wd-set). In this paper, the strong and weak domination numbers of comet, double comet, double star and theta graphs are given. The theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, MST construction and real-Time animation. © The authors.