## What are labels on graphs?

Labels are a kind of naming that can be applied to any node in the graph. They are a name only — and so labels are either present or absent. From graph database concepts: Labels are used to shape the domain by grouping nodes into sets where all nodes that have a certain label belongs to the same set.

What is adjacency in a graph?

In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal.

What is a weighted graph?

A weighted graph is a graph with edges labeled by numbers (called weights). In general, we only consider nonnegative edge weights. Sometimes, ∞ can also be allowed as a weight, which in optimization problems generally means we must (or may not) use that edge.

### What are graph labeling algorithms?

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.

What are labels used for?

Labels may be used for any combination of identification, information, warning, instructions for use, environmental advice or advertising. They may be stickers, permanent or temporary labels or printed packaging.

Why is it important to label a graph?

Graphs are an excellent way to make a visual representation of data that have been collected. However, without proper labeling, the graph won’t make sense. Therefore, make sure you label the x-axis and y-axis and title your graph so it can be understood by people without having to ask what it represents.

## What is an adjacency matrix explain?

An adjacency matrix is a way of representing a graph as a matrix of booleans (0’s and 1’s). A finite graph can be represented in the form of a square matrix on a computer, where the boolean value of the matrix indicates if there is a direct path between two vertices.

What is weighted graph give example?

As an example of a weighted graph, imagine you run an airline and you’d like a model to help you estimate fuel costs based on the routes you fly. In this example the nodes would be airports, edges would represent flights between airports, and the edge weight would be the estimated cost of flying between those airports.

### What is Alpha labeling in graph theory?

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 ) .

Why is label important?

Labelling is an important part of the marketing of a product. Labelling is essential as it helps to grab the attention of a customer It can be combined with packaging and can be used by marketers to encourage potential buyers to purchase the product. Packaging is also used for convenience and information transmission.

What is a graph labeling?

Graph labeling. In the mathematical discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to the edges or vertices, or both, of a graph.

## What is graceful labelling in graph theory?

A graceful labelling. Vertex labels are in black, edge labels in red. A graph is known as graceful when its vertices are labeled from 0 to |V|, the size of the graph, and this labelling induces an edge labelling from 1 to |E|.

What is a vertex-labeled graph?

In the mathematical discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to the edges or vertices, or both, of a graph. Formally, given a graph G = (V, E), a vertex labeling is a function of V to a set of labels. A graph with such a function defined is called a vertex-labeled graph.

What is a vertex labelling function?

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. Formally, given a graph G = (V, E), a vertex labelling is a function of V to a set of labels. A graph with such a function defined is called a vertex-labeled graph.