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The locating-chromatic number for Halin graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 1، دوره 2، شماره 1، شهریور 2017، صفحه 1-9 اصل مقاله (375.71 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2017.13577 | ||
| نویسندگان | ||
| I.A. Purwasih1؛ Edy T. Baskoro* 1؛ H. Assiyatun1؛ D. Suprijanto1؛ M. Baca2 | ||
| 1Institut Teknologi Bandung | ||
| 2Technical University in Koˇsice | ||
| چکیده | ||
| Let $G$ be a connected graph. Let $f$ be a proper $k$-coloring of $G$ and $\Pi=\{R_1,R_2,\ldots, R_k\}$ be an ordered partition of $V(G)$ into color classes. For any vertex $v$ of $G,$ define the {\em color code} $c_\Pi(v)$ of $v$ with respect to $\Pi$ to be a $k$-tuple $(d(v,R_1),d(v,R_2),\ldots,d(v,R_k)),$ where $d(v,R_i)= \text{min}\{d(v,x)|x\in R_i\}.$ If distinct vertices have distinct color codes, then we call $f$ a {\em locating coloring} of $G.$ The {\em locating-chromatic number} of $G$ is the minimum number $k$ such that $G$ admits a locating coloring with $k$ colors. In this paper, we determine a lower bound of the locating-chromatic number of Halin graphs. We also give the locating-chromatic number of a Halin graph of a double star. | ||
| کلیدواژهها | ||
| locating-chromatic number؛ Halin؛ double star | ||
| مراجع | ||
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