Bilangan Kromatik Ketakteraturan Lokal pada Graf Hasil Operasi Comb pada Graf Lintasan dengan Graf Unicyclic

Abstract

Suppose G(V,E) is a simple connected graph. V(G) is the set of vertex and E(G) is a set of edge. Let l:V(G)→{1,2,…k} the labeling function and w:V(G)→N local irregularity vertex coloring and w(u)=∑_(u∈N(u))▒〖l(v)〗. Minimum number of local irregularity vertex coloring of graph G is called local irregularity chromatic number, denote by χ_lis (G). The paper studies on local irregularity vertex coloring and chromatic number of comb operation of path graph and unicyclic graphs. The research resulted in four theorems about the irregularity local coloring operations of comb on path graphs and unicyclic graphs. A resulting theorem is that a tadpole graph (P_k ⊳_(v_1 ) T_(m,r) ), cricket graph (P_k ⊳_(v_1 ) Cr_(n,m) ), net graph (P_k ⊳_(v_1 ) N_(3,m) ), and peach graph (P_k ⊳_(v_1 ) C_m^n ).