A vertex-magic total labeling (VMTL) on a graph with vertices and edges is a one-to-one mapping from the vertices and edges onto the integers 1 , 2 , … , v + e so that the sum of the label on a vertex and the labels of its incident edges is constant, independent of the choice of vertex.

What is magic Labelling?

A vertex-magic total labeling (VMTL) on a graph with vertices and edges is a one-to-one mapping from the vertices and edges onto the integers 1 , 2 , … , v + e so that the sum of the label on a vertex and the labels of its incident edges is constant, independent of the choice of vertex.

What is the labeling of a graph?

In the mathematical discipline of graph theory, a graph labelling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. to a set of labels. In this case, the graph is called an edge-labeled graph.

What is the use of graph labeling?

Graph labeling is an assignment of integers to vertices or edges, or both, under certain conditions. In parallel with graph labeling, topological graph theory was introduced as the four-color map problem. It was finally proven in 1976 by using computerized checking.

Can edges of a graph be labeled?

A good edge-labelling of a graph is a labelling of its edges such that, for any ordered pair of vertices , there do not exist two paths from to with increasing labels.

What is Alpha labeling?

A graph admitting a graceful labeling is called a graceful graph. A graceful labeling is said to be an alpha labeling if there exists a number (called the boundary value) with the property that for every edge x y ∈ G with ρ ( x ) < ρ ( y ) it holds that ρ ( x ) ≤ λ < ρ ( y ) .

What is harmonious labeling?

A harmonious labeling on a graph G is an injection from. the vertices of G to the group of integers modulo k, where k. is the number of edges of G, that induces a bijection between. the edges of G and the numbers modulo k by taking the edge. label for an edge (x, y) to be the sum of the labels of the.

What are axis labels on a graph?

Axis labels are words or numbers that mark the different portions of the axis. Value axis labels are computed based on the data displayed in the chart. Category axis labels are taken from the category headings entered in the chart’s data range. Axis titles are words or phrases that describe the entire axis.

What is Alpha labeling in graph theory?

Is it labeled or Labelled?

Labeled and labelled are both correct spellings. Labeled is the preferred spelling in American English. Labelled is the preferred spelling in British English.

How many labeled graphs can n vertices have?

2
The number of labeled n-vertex simple undirected graphs is 2. The number of labeled n-vertex simple directed graphs is 2.

How do you label a bar graph?

Required bar graph titles include the name of the graph, the title of the vertical axes, and the title of the horizontal axes. It is important to title bar graphs carefully so the information makes sense and the graph is easy to read and understand.