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- W2238495544 abstract "A proper edge coloring of a simple graph $G$ is called a vertexdistinguishing edge coloring (vdec) if for any two distinct vertices $u$ and$v$ of $G$, the set of the colors assigned to the edges incident to $u$ differsfrom the set of the colors assigned to the edges incident to $v$. The minimumnumber of colors required for all vdecs of $G$ is denoted by $chi,'_s(G)$called the vdec chromatic number of $G$. Let $n_d(G)$ denote the number ofvertices of degree $d$ in $G$. In this note, we show that a tree $T$ with$n_2(T)leq n_1(T)$ holds $chi,'_s(T)=n_1(T)+1$ if its diameter $D(T)=3$ orone of two particular trees with $D(T) =4$, and $chi,'_s(T)=n_1(T)$otherwise; furthermore $chi,'_{es}(T)=chi,'_s(T)$ when $|E(T)|leq2(n_1(T)+1)$, where $chi,'_{es}(T)$ is the equitable vdec chromatic number of$T$." @default.
- W2238495544 created "2016-06-24" @default.
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- W2238495544 date "2016-01-09" @default.
- W2238495544 modified "2023-09-27" @default.
- W2238495544 title "A Note On Vertex Distinguishing Edge colorings of Trees" @default.
- W2238495544 hasPublicationYear "2016" @default.
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