The edge-distinguishing chromatic number of petal graphs, chorded cycles, and spider graphs
نویسندگان
چکیده
The edge-distinguishing chromatic number (EDCN) of a graph $G$ is the minimum positive integer $k$ such that there exists vertex coloring $c:V(G)\to\{1,2,\dotsc,k\}$ whose induced edge labels $\{c(u),c(v)\}$ are distinct for all edges $uv$. Previous work has determined EDCN paths, cycles, and spider graphs with three legs. In this paper, we determine petal two petals loop, cycles one chord, four These achieved by embedding into looped complete graphs.
منابع مشابه
The distinguishing chromatic number of bipartite graphs of girth at least six
The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...
متن کاملThe 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 کاملThe Distinguishing Chromatic Number of Kneser Graphs
A labeling f : V (G) → {1, 2, . . . , d} of the vertex set of a graph G is said to be proper d-distinguishing if it is a proper coloring of G and any nontrivial automorphism of G maps at least one vertex to a vertex with a different label. The distinguishing chromatic number of G, denoted by χD(G), is the minimum d such that G has a proper d-distinguishing labeling. Let χ(G) be the chromatic nu...
متن کاملIndependent cycles and chorded cycles in graphs
In this paper, we investigate sufficient conditions on the neighborhood of independent vertices which imply that a graph contains k independent cycles or chorded cycles. This is related to several results of Corrádi and Hajnal, Justesen, Wang, and Faudree and Gould on graphs containing k independent cycles, and Finkel on graphs containing k chorded cycles. In particular, we establish that if in...
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 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: EJGTA : Electronic Journal of Graph Theory and Applications
سال: 2022
ISSN: ['2338-2287']
DOI: https://doi.org/10.5614/ejgta.2022.10.2.5