On friendly index sets of the edge-gluing of complete graph and cycles
نویسندگان
چکیده
منابع مشابه
full 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 کاملFull 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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15 صفحه اولOn friendly index sets of cycles with parallel chords
Let G be a graph with vertex set V(G) and edge set E(G), and let A be an abelian group. A labeling f: V(G) A induces an edge labeling f"': E(G) A defined by f"'(xy) = f(x) + fey), for each edge xy e E(G). For i e A, let vt<i) = card { v e V(G) : f(v) = i} and er(i) = card ( e e E(G) : f"'(e) = i}. Let c(f) = {Iet<i) etG)1 : (i, j) e A x A}. A labeling f of a graph G is said to be A friendly if...
متن کاملOn the Chromatic Uniqueness of Edge-Gluing of Complete Bipartite Graphs and Cycles
In this paper, it is shown that the graph obtained by overlapping the cycle and the complete tripartite graph at an edge is uniquely determined by its chromatic polynomial. ) 3 ( ≥ m Cm 2 , 2 , 2 K Let G be a finite graph with neither loops nor multiple edges and let ) ; ( λ G P denote its chromatic polynomial. Then G is said to be chromatically unique if ) ; ( ) ; ( λ λ G Y P = implies that Y ...
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2016
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2016.06.004