What is meant by graceful labeling?
What is meant by graceful labeling?
A graceful labeling (or graceful numbering) is a special graph labeling of a graph on edges in which the nodes are labeled with a subset of distinct nonnegative integers from 0 to and the graph edges are labeled with the absolute differences between node values.
What is a graceful tree?
Graceful trees Graphs that are trees are simple, connected, and acyclic. This implies that trees exhibit the property V=E+1 where V is the number of vertices and E is the number of edges.
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 is Labelling in graph theory?
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.
Who introduced graceful labeling?
The term “graceful” was introduced by Golomb [12] in 1972. Rosa showed that if every tree is graceful, then Ringel’s conjecture holds.
What is Alpha labeling?
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 ) . Obviously, must be bipartite to allow an alpha labeling.
What is label in a figure?
A caption (legend) must be provided for each figure. Captions must be placed on a separate page at the end of the manuscript. If a figure part such as (a) or (b) is referred to in a caption, that figure part must be labeled.
What is a caterpillar in graph?
A caterpillar graph, caterpillar tree, or simply “caterpillar,” is a tree in which every graph vertex is on a central stalk or only one graph edge away from the stalk (in other words, removal of its endpoints leaves a path graph; Gallian 2007).
How do you label figures?
Figure captions Figures should be labeled with a number followed by a descriptive caption or title. Captions should be concise but comprehensive. They should describe the data shown, draw attention to important features contained within the figure, and may sometimes also include interpretations of the data.
What are Caterpillar trees?
Equivalent characterizations. The following characterizations all describe the caterpillar trees: They are the trees for which removing the leaves and incident edges produces a path graph. They are the trees in which there exists a path that contains every vertex of degree two or more.
What is a figure label?
Figure Title A figure title informs the viewer what they should. learn from the graph or figure. This should not be a. full sentence or a statement of the axis titles; rather, it should provide context for the figure.
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. Name the bar graph.