On Locating Chromatic Number of Cubic Graph with Tree Cycle, Cn,2n,n, for n=3,4,5
نویسندگان
چکیده
Let G = (V(G), E(G)) be a connected graph and is coloring of G. Π {C1, C2, ...,Ck}, where Ci the partition vertex in which colored i with 1 ≥ k. The representation v for called color code, denoted CΠ(v) ordered pair k-element namely, (d(v, C1), d(v, C2), ..., Ck)), Ci)= mind{d(v, x)|xεCi} If every have different c locating coloring. minimum number colors used chromatic locating, notated by XL(G). In this paper, we will determine cubic Cn,2n,n, n=3,4,5.
منابع مشابه
The locating-chromatic number for Halin graphs
Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
متن کاملOn locating-chromatic number of complete n -ary tree
Let c be a vertex k -coloring on a connected graph G(V,E) . Let Π = {C1, C2, ..., Ck} be the partition of V (G) induced by the coloring c . The color code cΠ(v) of a vertex v in G is (d(v, C1), d(v, C2), ..., d(v, Ck)), where d(v, Ci) = min{d(v, x)|x ∈ Ci} for 1 ≤ i ≤ k. If any two distinct vertices u, v in G satisfy that cΠ(u) 6= cΠ(v), then c is called a locating k-coloring of G . The locatin...
متن کاملThe locating chromatic number of the join of graphs
Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Pi$ is defined to be the ordered $k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$, where $d(v,V_i)=min{d(v,x):~xin V_i}, 1leq ileq k$. If distinct...
متن کاملTrees with Certain Locating-Chromatic Number
The locating-chromatic number of a graph can be defined as the cardinality of a minimum resolving partition of the vertex set such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in are not contained in the same partition class. In this case, the coordinate of a vertex in is expressed in terms of the distances of to all partition classe...
متن کاملtotal dominator chromatic number of a graph
given a graph $g$, the total dominator coloring problem seeks aproper coloring of $g$ with the additional property that everyvertex in the graph is adjacent to all vertices of a color class. weseek to minimize the number of color classes. we initiate to studythis problem on several classes of graphs, as well as findinggeneral bounds and characterizations. we also compare the totaldominator chro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2021
ISSN: ['1742-6588', '1742-6596']
DOI: https://doi.org/10.1088/1742-6596/1940/1/012020