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Vertex-magic total labeling of the union of suns
(Ars Combinatoria, 2012)
Let $G$ be a graph with vertex set $V=V(G)$ and edge set $E=E(G)$ and
let $e=\vert E(G) \vert$ and $v=\vert V(G) \vert$. A one-to-one map $\lambda$ from $V\cup E$ onto the integers $\{ 1,2, ..., v+e \}$ is called {\it ...
On Total Vertex Irregularity Strength Cocktail Party Graphs
(Jurnal Ilmu Dasar, 2011-01)
A vertex irregular total k-labeling of a graph G is a function λ from both the vertex and the edge sets to {1,2,3,,k} such that for every pair of distinct vertices u and x, λ(u)+ Σλ(uv) ≠ λ(x)+ Σλ(xy). The integer k is ...
Vertex-magic total labelings of disconnected graphs
(Journal of Prime Research in Mathematics, 2006)
Let $G$ be a graph with vertex set $V=V(G)$ and edge set $E=E(G)$ and
let $e=\vert E(G) \vert$ and $v=\vert V(G) \vert$.
A one-to-one map $\lambda$ from $V\cup E$ onto the integers
$\{ 1,2, ..., v+e \}$ is called {\it ...
Total vertex irregularity strength of wheel related graphs
(Australasian Journal of Combinatorics, 2011)
For a simple graph G with vertex set V (G) and edge set E(G), a labeling φ : V (G) ∪ E(G) → {1, 2, . . . , k} is called a vertex irregular total klabeling of G if for any two different vertices x and y, their weights wt(x) ...
Total Vertex Irregularity Strength of the Disjoint Union of Sun Graphs
(International Journal of Combinatorics, 2012)
A vertex irregular total $k$-labeling of a graph $G$ with vertex set $V$ and edge set $E$ is an assignment of positive integer labels $\{1,2,...,k\}$ to both vertices and edges so that the weights calculated at vertices ...
Most wheel related graphs are not vertex magic
(Utilitas Math., 2008)
Suppose $G$ is a finite graph with vertex-set $V(G)$ and edge-set $E(G)$. A one-to-one map $\lambda$ from $V(G)\cup E(G)$ onto the integers $1,2,3, \dots, |V(G)|+|E(G)|$ is called a {\it vertex-magic total labeling}, if ...
On the Existence of Non-Diregular Digraphs of Order Two less than the Moore Bound
(Jurnal Ilmu Dasar, 2011-01)
A communication network can be modelled as a graph or a directed graph, where each processing element is represented by a vertex and the connection between two processing elements is represented by an edge (or, in case of ...
On super edge-magic total labeling of banana trees
(Utilitas Math., 2009)
Let G1;G2;...;Gn be a family of disjoint stars. The tree obtained by joining a new vertex a to one pendant vertex of each star is called a banana tree. In this paper we consider the super edge magic total labeling of banana ...
On the partition dimension and connected partition dimension of wheels
(Ars Combinatoria, 2007)