منابع مشابه
On friendly index sets of 2-regular graphs
Let G be a graph with vertex set V and edge set E , and let A be an abelian group. A labeling f : V → A induces an edge labeling f ∗ : E → A defined by f (xy) = f (x) + f (y). For i ∈ A, let v f (i) = card{v ∈ V : f (v) = i} and e f (i) = card{e ∈ E : f (e) = i}. A labeling f is said to be A-friendly if |v f (i)−v f ( j)| ≤ 1 for all (i, j) ∈ A× A, and A-cordial if we also have |e f (i) − e f (...
متن کاملproduct-cordial index and friendly index of regular graphs
let $g=(v,e)$ be a connected simple graph. a labeling $f:v to z_2$ induces two edge labelings $f^+, f^*: e to z_2$ defined by $f^+(xy) = f(x)+f(y)$ and $f^*(xy) = f(x)f(y)$ for each $xy in e$. for $i in z_2$, let $v_f(i) = |f^{-1}(i)|$, $e_{f^+}(i) = |(f^{+})^{-1}(i)|$ and $e_{f^*}(i) = |(f^*)^{-1}(i)|$. a labeling $f$ is called friendly if $|v_f(1)-v_f(0)| le 1$. for a friendly labeling $f$ of...
متن کاملFull friendly index sets of cylinder graphs
Let G = (V,E) be a connected simple graph. A labeling f : V → Z2 induces an edge labeling f : E → Z2 defined by f(xy) = f(x) + f(y) for each xy ∈ E. For i ∈ Z2, let vf (i) = |f−1(i)| and ef(i) = |(f+)−1(i)|. A labeling f is called friendly if |vf (1) − vf(0)| ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if(G) = ef (1) − ef(0). The set {if(G) | f is a...
متن کاملfull edge-friendly index sets of complete bipartite graphs
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(...
متن کاملOn Edge-Balance Index Sets of Regular Graphs
In a bi-racial country, it is desired that the numbers of government ministers from the two races should differ by at most one for fairness. Moreover, the numbers of pairs of ministries which interact directly with each other and both headed by ministers of one race should differ by at most one from that of the other race. One can naturally model the above social phenomenon by a graph labeling ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.10.018