This research aims to determine the pattern of dominance side contraction numbers
in banana tree graphs and fireworks graphs. Banana tree graph B_n,,k is  a graph obtained by connecting one leaf from each n-copies  of a k star graph with one vertex that is different from all the star graphs. The fireworks graph  is a tree that is similar to the caterpillar graph, the difference lies in the backbone node n which is connected to the earring node k from the caterpillar graph. The dominating number is denoted by γ ( G ) is the smallest cardinality of a dominating set. Domination set The minimum is a dominating set from which no points can be removed without changing its dominance. Domination contraction number of a graph ctγ ( G ) is defined as the minimum number of edges that must be contracted to reduce the dominance number .

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