Bilangan Kromatik Ketakteraturan Lokal Inklusif pada Keluarga Graf Pohon

Abstract

The chromatic number of inclusive local irregularity is the minimum colors obtained from the coloring and denoted by 𝜒_𝑙𝑖𝑠^𝐼(𝐺). Let 𝑙: 𝑉(𝐺) → {1,2,3, … , 𝑝} is a label function and 𝑤^𝐼: 𝑉(𝐺) → ℕ is a weight function, with 𝑤^𝐼(𝑢) =∑𝑣∈𝑁(𝑢) 𝑙(𝑣) + 𝑙(𝑢), then 𝜒_𝑙𝑖𝑠^𝐼(𝐺) = |𝑤^𝐼(𝑢)|. The analyse of chromatic number of inclusive local irregularity on the tree graphs family is limited in scope. The aim of this study is to find the chromatic number of inclusive local irregularity on the tree graphs family consists of firecracker graph (𝐹𝑛,𝑚), double broom graph (𝐷𝐵𝑟𝑛,𝑚), centipede graph (𝐶𝑃𝑛),banana tree graph (𝐵𝑡𝑘,𝑚), complete binary graph (𝑇𝑘,𝑑) and lobster graph (𝐿𝑛,𝑠1,𝑠2). The method of this study are pattern detection method and axiomatic deduction method. The result of this study is a theorem on firecracker graph, three theorems on double broom graph, a theorem on centipede graph, three theorems on banana tree graph, a theorem on complete binary graph and two theorems on lobster graph. Keywords: chromatic number, an inclusive local irregularity, tree graphs family