On locating-chromatic number for certain lobster graph.

Concept of locating-chromatic number for a graph is one interesting concept in graph theory. This concept is married between two concept which old and new concept. That concept are coloring and dimension partition for a graph. The locating-chromatic number is development research in graph theory. Let G(V(G),E(G)) is a connected graph. Let ∏ = { S 1 , S 2 ,... , S k } and color code c π (v) = (d (v , S 1) , d (v , S 2) ,... , d (v , S k)) where d (v , S i) = min { d (v , x) | x ∈ s i } with 1≤i≤k. If every vertices of G have distinct color codes, then c is called a locating coloring of G. The minimum number of colors used in locating coloring of G is called locating chromatic number of G denoted by XL(G). In this paper we obtain the locating chromatic number for certain lobster graph Ln,m,1 especially for m=3,4,5. [ABSTRACT FROM AUTHOR]