Pewarnaan Titik Ketakteraturan Lokal pada Hasil Operasi Amalgamasi Titik Graf Lintasan

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October 26, 2023

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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)β†’{1,2, … ,π‘˜} as label function and weight function 𝑀 : 𝑉(𝐺)→𝑁 is desined as 𝑀(𝑒)=Ξ£π‘£βˆˆπ‘(𝑒)𝑙(𝑣). The function 𝑀 is called local irregularity vertex coloring if: (i) π‘œπ‘π‘‘(𝑙)=π‘šπ‘–π‘› (π‘šπ‘Žπ‘˜π‘  (𝑙𝑖) ;𝑙𝑖 𝑖𝑠 π‘™π‘Žπ‘π‘’π‘™ π‘“π‘’π‘›π‘π‘‘π‘–π‘œπ‘›) and (ii) for every 𝑒𝑣 ∈ 𝐸(𝐺),𝑀(𝑒) β‰  𝑀(𝑣). The chromatic number of local irregularity vertex coloring denoted by πœ’π‘™π‘–π‘ (𝐺) is defined as πœ’π‘™π‘–π‘ (𝐺)=π‘šπ‘–π‘›{|𝑀(𝑉(𝐺))|;𝑀 𝑖𝑠 π‘™π‘œπ‘π‘Žπ‘™ π‘–π‘Ÿπ‘Ÿπ‘’π‘”π‘’π‘™π‘Žπ‘Ÿπ‘–π‘‘π‘¦ π‘£π‘’π‘Ÿπ‘‘π‘’π‘₯ π‘π‘œπ‘™π‘œπ‘Ÿπ‘–π‘›π‘”}. 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 (π‘Žπ‘šπ‘Žπ‘™(𝑃𝑛 ,𝑣,π‘š)). 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.

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