Bilangan Independent Domination pada Graf Caterpillar dan Graf Lobster Teratur

Abstract

Let G=(V,E) be a simple graph with a vertex set V(G) and edge vertex E(G), let I⊆V(G). Set I is called independent domination if there is no vertices are adjacent in I and for all v∈V(G) \ I are adjacent to vertex in I. Minimum size of indepedent domination set in G called independent domination number i(G). Let C_(n_r ) be the regular catepillar graph with r central vertex and n support vertex, in addition L_(n ) (q;r) be the regular lobster graph with n backbone vertex, q hand vertex, and r finger vertex. In this research, it is shown that C_(n_r ) and L_(n ) (q;r) has a domination number and an independent domination number. The domination number of C_(n_r ) is 〖γ(C〗_(n_r ))=r. The independent domination number of C_(n_r ) for r is an even number is 〖i(C〗_(n_r ))=r/2(1+n) and for r is an odd number is 〖i(C〗_(n_r ))=((r-1)(n+1))/2+1. It has also been proven that in L_(n ) (q;r), the domination number is the same as the independent domination number of this graph, γ(L_(n ) (q;r))=i(L_(n ) (q;r))=nq.