Pewarnaan Titik Ketakteraturan Lokal pada Hasil Operasi Amalgamasi Titik Graf Lintasan

Abstract

Definition of graph is set pair (𝑉(𝐺),𝐸(𝐺)) where 𝑉(𝐺) is vertex set and 𝐸(𝐺) is edge set. A maping 𝐼 : 𝑉(𝐺)→{1,2, … ,𝑘} as label function and weight function 𝑤 : 𝑉(𝐺)→𝑁 is desined as 𝑤(𝑢)=Σ𝑣∈𝑁(𝑢)𝑙(𝑣). The function 𝑤 is called local irregularity vertex coloring if: (i) 𝑜𝑝𝑡(𝑙)=𝑚𝑖𝑛 (𝑚𝑎𝑘𝑠 (𝑙𝑖) ;𝑙𝑖 𝑖𝑠 𝑙𝑎𝑏𝑒𝑙 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛) and (ii) for every 𝑢𝑣 ∈ 𝐸(𝐺),𝑤(𝑢) ≠ 𝑤(𝑣). The chromatic number of local irregularity vertex coloring denoted by 𝜒𝑙𝑖𝑠(𝐺) is defined as 𝜒𝑙𝑖𝑠(𝐺)=𝑚𝑖𝑛{|𝑤(𝑉(𝐺))|;𝑤 𝑖𝑠 𝑙𝑜𝑐𝑎𝑙 𝑖𝑟𝑟𝑒𝑔𝑢𝑙𝑎𝑟𝑖𝑡𝑦 𝑣𝑒𝑟𝑡𝑒𝑥 𝑐𝑜𝑙𝑜𝑟𝑖𝑛𝑔}. The method used in this paper is pattern recognition and axiomatic deductive method. In this paper, we learn local irregularity vertex coloring of vertex amalgamation of path graph and determine the chromatic number on local irregularity vertex coloring of vertex amalgamation of path graph. This paper use vertex amalgamation of path graph (𝑎𝑚𝑎𝑙(𝑃𝑛 ,𝑣,𝑚)). The result of this study are expected to be used as basic studies and science development as well as applications related to local irregularity vertex coloring of vertex amalgamation of path graph.