On Locating Chromatic Number of H = Pm ∪ Wn
نویسندگان
چکیده
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...
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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...
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The paper generalizes the notion of locating-chromatic number of a graph such that it can be applied to disconnected graphs as well. In this sense, not all the graphs will have finite locating-chromatic numbers. We derive conditions under which a graph has a finite locating-chromatic number. In particular, we determine the locatingchromatic number of a uniform linear forest, namely a disjoint u...
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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 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...
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2021
ISSN: 1742-6588,1742-6596
DOI: 10.1088/1742-6596/1742/1/012024