Pewarnaan Titik Ketakteraturan Lokal pada Hasil Operasi Amalgamasi Titik Graf Lintasan

Definition of graph is set pair (𔑉(ð”º),ð”¸(ð”º)) where 𔑉(ð”º) is vertex set and ð”¸(ð”º) is edge set. A maping 𔼠: 𔑉(ð”º)→{1,2, ... ,𔑘} as label function and weight function 𔑤 : 𔑉(ð”º)→𔑠is desined as 𔑤(𔑢)=Σ_{𔑣∈ð”‘(𔑢)}𔑙(𔑣). The function 𔑤 is called local irregularity vertex coloring if: (i) 𔑜𔑔𔑡(𔑙)=𔑚𔑖𔑛 (𔑚𔑎𔑘𔑠 (𔑙_𔑖) ;𔑙_𔑖 𔑖𔑠 𔑙𔑎ð”‘𔑒𔑙 𔑓𔑢𔑛ð”‘𔑡𔑖𔑜𔑛) and (ii) for every 𔑢𔑣 ∈ ð”¸(ð”º),𔑤(𔑢) ≠ 𔑤(𔑣). The chromatic number of local irregularity vertex coloring denoted by 𔜒_{𔑙𔑖ð”‘} (ð”º) is defined as 𔜒_{𔑙𔑖ð”‘} (ð”º)=𔑚𔑖𔑛{|𔑤(𔑉(ð”º))|;𔑤 𔑖𔑠 𔑙𔑜ð”‘𔑎𔑙 𔑖𔑟𔑟𔑒𔑔𔑢𔑙𔑎𔑟𔑖𔑡𔑦 𔑣𔑒𔑟𔑡𔑒𔑥 ð”‘𔑜𔑙𔑜𔑟𔑖𔑛𔑔}. 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 (𔑎𔑚𔑎𔑙(𔑃_𔑛 ,𔑣,𔑚)). 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.