A k-circular-distance-two labeling (or k-c-labeling) of a simple graph G is a vertex-labeling, using the labels 0, 1, 2, · · · , k − 1, such that the “circular difference” (mod k) of the labels for adjacent vertices is at least two, and for vertices of distance-two apart is at least one. The σ-number, σ(G), of a graph G is the minimum k of a k-c-labeling of G. For any given positive integers n ...

A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if either ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 if ( ) ( ) f u f v , then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial ...

Let N0 be the set of all non-negative integers, let X N0 and P(X) be the the power set of X. An integer additive set-labeling (IASL) of a graph G is an injective function f : V (G) ! P(N0) such that the induced function f+ : E(G) ! P(N0) is defined by f+(uv) = f(u) + f(v), where f(u) + f(v) is the sum set of f(u) and f(v). An IASL f is said to be an integer additive set-indexer (IASI) of a grap...

In this paper, we are studying vertex-magic total labelings of simple graphs. We introduce a procedure called mutation which transforms one labeling into another by swapping sets of edges among vertices. The result of a mutation may be a different labeling of the same graph or a labeling of a different graph. Mutation proves to be a remarkably fruitful process— for example we are able to genera...

A graph G is said to be A-magic if there is a labeling l : E(G) −→ A − {0} such that for each vertex v, the sum of the labels of the edges incident with v are all equal to the same constant; that is, l+(v) = c for some fixed c ∈ A. In general, a graph G may admit more than one labeling to become A-magic; for example, if |A| > 2 and l : E(G) −→ A − {0} is a magic labeling of G with sum c, then l...

For a simple graph G, a vertex labeling φ : V (G) → {1, 2, · · · , k} is called k-labeling. The weight of an edge xy in G, denoted by wπ(xy), is the sum of the labels of end vertices x and y, i.e. wφ(xy) = φ(x) + φ(y). A vertex k-labeling is defined to be an edge irregular k-labeling of the graph G if for every two different edges e and f , there is wφ(e) 6= wφ(f). The minimum k for which the g...

Let G be a graph and f : V (G) → {1, 2, 3, . . . , p+ q} be an injection. For each edge e = uv and an integer m ≥ 2, the induced Smarandachely edge m-labeling f∗ S is defined by f ∗ S(e) = ⌈ f(u) + f(v) m ⌉ . Then f is called a Smarandachely super m-mean labeling if f(V (G))∪ {f∗(e) : e ∈ E(G)} = {1, 2, 3, . . . , p+ q}. Particularly, in the case of m = 2, we know that f ∗(e) =    f(u)+f(v) ...

Let G(V, E) be a graph with order n no component of 2. An edge k-labeling α: E(G) →{1,2,…,k} is called modular irregular G if the corresponding weight function wt_ α:V(G) → Z_n defined by α(x) =Ʃ_(xyϵE(G)) α(xy) bijective. The value wt_α(x) vertex x. Minimum k such that has irregularity strength G. In this paper, we define labeling on C_n⊙mK_1. Furthermore, determine C_n⊙mK_1.Keywords: corona p...

A total labeling of a graph G is a bijection from the vertex set and edge set of G onto the set {1, 2, . . . , |V (G)| + |E(G)|}. Such a labeling ξ is vertex-antimagic (edge-antimagic) if all vertex-weights wtξ(v) = ξ(v) + ∑ vu∈E(G) ξ(vu), v ∈ V (G), (all edge-weights wtξ(vu) = ξ(v) + ξ(vu) + ξ(u), vu ∈ E(G)) are pairwise distinct. If a labeling is simultaneously vertex-antimagic and edge-antim...

We present a program package to generate homogeneous random graphs with probabilities prescribed by the user. The statistical weight of a labeled graph α is given in the form W(α)=∏Ni=1 p(qi), where p(q) is an arbitrary user function and qi are the degrees of the graph nodes. The program can be used to generate two types of graphs (simple graphs and pseudo-graphs) from three types of ensembles ...