$Z_k$-Magic Labeling of Some Families of Graphs
Authors
Abstract:
For any non-trivial abelian group A under addition a graph $G$ is said to be $A$-textit{magic} if there exists a labeling $f:E(G) rightarrow A-{0}$ such that, the vertex labeling $f^+$ defined as $f^+(v) = sum f(uv)$ taken over all edges $uv$ incident at $v$ is a constant. An $A$-textit{magic} graph $G$ is said to be $Z_k$-magic graph if the group $A$ is $Z_k$ the group of integers modulo $k$. These $Z_k$-magic graphs are referred to as $k$-textit{magic} graphs. In this paper we prove that the total graph, flower graph, generalized prism graph, closed helm graph, lotus inside a circle graph, $Godotoverline{K_m}$, $m$-splitting graph of a path and $m$-shadow graph of a path are $Z_k$-magic graphs.
similar resources
Totally magic cordial labeling of some graphs
A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...
full texttotally magic cordial labeling of some graphs
a graph g is said to have a totally magic cordial labeling with constant c if there exists a mapping f : v (g) ∪ e(g) → {0, 1} such that f(a) + f(b) + f(ab) ≡ c (mod 2) for all ab ∈ e(g) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. in this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...
full textEdge-Magic Labeling of some Graphs
An edge magic labeling f of a graph with p vertices and q edges is a bijection f: V ∪ E → {1, 2, ..., p + q } such that there exists a constant s for any (x, y) in E satisfying f(x) + f(x, v) + f(y)= s. In this paper, the edge-magic labelings of ncm and some other graphs are discussed.
full textGroup distance magic labeling of some cycle-related graphs
Let G = (V,E) be a graph and Γ an abelian group, both of order n. A group distance magic labeling of G is a bijection : V → Γ for which there exists μ ∈ Γ such that ∑x∈N(v) (x) = μ for all v ∈ V, where N(v) is the neighborhood of v. Froncek [Australas. J. Combin. 55 (2013), 167–174] showed that the cartesian product Cm Cn, m,n ≥ 3 is a Zmn-distance magic graph if and only if mn is even. In this...
full textOdd Harmonious Labeling of Some New Families of Graphs
A graph G(p, q) is said to be odd harmonious if there exists an injection f : V (G) → {0, 1, 2, · · · , 2q − 1} such that the induced function f∗ : E(G) → {1, 3, · · · , 2q − 1} defined by f∗(uv) = f(u) + f(v) is a bijection. A graph that admits odd harmonious labeling is called odd harmonious graph. In this paper, we prove that shadow and splitting of graph K2,n, Cn for n ≡ 0 (mod 4), the grap...
full textEdge pair sum labeling of some cycle related graphs
Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex v and f*(V (G)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} U {±k(p+1)/2} according as p is even or o...
full textMy Resources
Journal title
volume 50 issue issue 2
pages 1- 12
publication date 2018-12-30
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023