full edge-friendly index sets of complete bipartite graphs
نویسندگان
چکیده
let $g=(v,e)$ be a simple graph. an edge labeling $f:eto {0,1}$ induces a vertex labeling $f^+:vtoz_2$ defined by $f^+(v)equiv sumlimits_{uvin e} f(uv)pmod{2}$ for each $v in v$, where $z_2={0,1}$ is the additive group of order 2. for $iin{0,1}$, let $e_f(i)=|f^{-1}(i)|$ and $v_f(i)=|(f^+)^{-1}(i)|$. a labeling $f$ is called edge-friendly if $|e_f(1)-e_f(0)|le 1$. $i_f(g)=v_f(1)-v_f(0)$ is called the edge-friendly index of $g$ under an edge-friendly labeling $f$. the full edge-friendly index set of a graph $g$ is the set of all possible edge-friendly indices of $g$. full edge-friendly index sets of complete bipartite graphs will be determined.
منابع مشابه
Full Edge-friendly Index Sets of Complete Bipartite Graphs
Let G = (V,E) be a simple graph. An edge labeling f : E → {0, 1} induces a vertex labeling f : V → Z2 defined by f(v) ≡ ∑ uv∈E f(uv) (mod 2) for each v ∈ V , where Z2 = {0, 1} is the additive group of order 2. For i ∈ {0, 1}, let ef (i) = |f−1(i)| and vf (i) = |(f+)−1(i)|. A labeling f is called edge-friendly if |ef (1) − ef (0)| ≤ 1. If (G) = vf (1) − vf (0) is called the edge-friendly index o...
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let g=(v,e) be a simple graph. an edge labeling f:e to {0,1} induces a vertex labeling f^+:v to z_2 defined by $f^+(v)equiv sumlimits_{uvin e} f(uv)pmod{2}$ for each $v in v$, where z_2={0,1} is the additive group of order 2. for $iin{0,1}$, let e_f(i)=|f^{-1}(i)| and v_f(i)=|(f^+)^{-1}(i)|. a labeling f is called edge-friendly if $|e_f(1)-e_f(0)|le 1$. i_f(g)=v_f(1)-v_f(0) is called the edge-f...
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عنوان ژورنال:
transactions on combinatoricsجلد ۶، شماره ۲، صفحات ۷-۱۷
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