With the fast development of networks, one has to focus on security information running in real networks. A technology that might be able resist attacks equipped with AI techniques and quantum computers is so-called topological graphic password coding. In order further study coding, we use multiple constraints graph colorings labelings propose 6C-labeling, 6C-complementary labeling, its recipro...

In graph theory, a graceful labeling of a graph G = (V, E) with n vertices and m edges is a labeling of its vertices with distinct integers between 0 and m inclusive, such that each edge is uniquely identified by the absolute difference between its endpoints. In this paper, the well-known graceful labeling problem of graphs is represented as an optimization problem, and an algorithm based on An...

ABSTRACT: A difference labeling of a graph G is realized by assigning distinct integer values to its vertices and then associating with each edge the absolute difference of those values assigned to its end vertices. A decomposition of labeled graph into parts, each part containing the edge having a commonweight is called a common – weight decomposition. In this paper we investigate the existenc...

In this paper we discuss cordial labeling in context of barycentric subdivision of shell graph, complete bipartite graph Kn,n and wheel graph. AMS subject classification: 05C78.

An edge magic total labeling of a graph with p vertices and q edges is a bijection from the set of vertices and edges to 1, 2, . . . , p+ q such that for every edge the sums of the label of the edge and the label of its two end vertices are constant. Otherwise if the sum is distinct, it is said to be an edge-antimagic total labeling. A graph is called edgeantimagic if it admits edge-antimagic t...

Let G be a graph of size n with vertex set V (G) and edge set E(G). A ρ-labeling of G is a one-to-one function h : V (G) → {0, 1, . . . , 2n} such that {min{|h(u)−h(v)|, 2n+1−|h(u)−h(v)|} : {u, v} ∈ E(G)} = {1, 2, . . . , n}. Such a labeling of G yields a cyclic G-decomposition of K2n+1. It is conjectured by El-Zanati and Vanden Eynden that every 2-regular graph G admits a ρ-labeling. We show t...

The even graceful labeling of a graph G with q edges means that there is an injection f : V(G) to { 0,1,1,1,2,...,2q+i/i= 1 to n} such that when each edge uv is assigned the label |f(u) – f(v)| the resulting edge labels are {1,3,5,...,2q-1}. A graph which admits an edge odd graceful labeling is called an edge-odd graceful graph. In this paper, the edge odd gracefulness of paths p1, p2, p3,..., ...

For a graph G = (V,E) and a binary labeling (coloring) f : V (G) → Z2, let vf (i) = |f−1(i)|. f is said to be friendly if |vf (1) − vf (0)| ≤ 1. The labeling f : V (G) → Z2 induces an edge labeling f∗ : E(G) → Z2 defined by f∗(xy) = |f(x)− f(y)| ∀xy ∈ E(G). Let ef (i) = |f∗−1(i)|. The friendly index set of the graph G, denoted by FI(G), is defined by FI(G) = {|ef (1)− ef (0)| : f is a friendly ...

An L(2, 1)-labeling (or distance two labeling) of a graph G is a function f from the vertex set V (G) to the set of all nonnegative integers such that |f(x) − f(y)| ≥ 2 if d(x, y) = 1 and |f(x) − f(y)| ≥ 1 if d(x, y) = 2. The L(2, 1)-labeling number λ(G) of G is the smallest number k such that G has an L(2, 1)-labeling with max{f(v) : v ∈ V (G)} = k. In this paper we completely determine the λ-...

The need of processing graph reachability queries stems from many applications that manage complex data as graphs. The applications include transportation network, Internet traffic analyzing, Web navigation, semantic web, chemical informatics and bio-informatics systems, and computer vision. A graph reachability query, as one of the primary tasks, is to find whether two given data objects, u an...