In this video we cover examples of types of trees that are often encountered in graph theory. A lobster graph, lobster tree, or simply lobster, is a tree having the property that the removal of leaf nodes leaves a caterpillar graph gallian 2007. This partial list of graphs contains definitions of graphs and graph families which are known by particular names, but do not have a wikipedia article of their own. A lobster is a tree in which the removal of leaves pendent vertices. A rooted tree has one point, its root, distinguished from others. What are some good books for selfstudying graph theory. In graph theory, a caterpillar or caterpillar tree is a tree in which all the vertices are within. Randomblockgraph, randomlobster, randomtriangulation.
A helm graph, denoted h n is a graph obtained by attaching a single edge and node to each node of the outer circuit of a wheel graph w n. A lobster graph is a tree in which all the vertices are within distance 2 of a central path. In this video i define a tree and a forest in graph theory. If a tree t is not a caterpillar but zt is, then t is called a lobster.
The various kinds of data structures referred to as trees in computer science have underlying graphs that are trees in graph theory, although such data structures are generally rooted trees. Bermond19 conjectured that lobsters are graceful a lobster is a tree with the property that the. Graceful labeling of different classes of lobsters connected in a. Graph theory by reinhard diestel, introductory graph theory by gary chartrand, handbook of graphs and networks. In other words, any connected graph without simple cycles is a tree. Graph and digraphs, 5th edition, by chartrand, lesniak, and zhang. Tree graph theory project gutenberg selfpublishing. Diestel is excellent and has a free version available online. See the file license for the licensing terms of the book. Graph labeling is an assignment of numbers to the vertices or edges or both subject to. Free graph theory books download ebooks online textbooks.
This is an introductory book on algorithmic graph theory. It is not the easiest book around, but it runs deep and has a nice unifying theme of studying how. It is a graduate level text and gives a good introduction to many different topics in graph theory. Then a graph g is graceful if there exists a labeling of its vertices. Discrete mathematics graph theory trees lobster graph. Chapter 3 graceful and harmonious labelings shodhganga. The mathematical prerequisites for this book, as for most graph theory texts, are minimal. Graph theory is one of the branches of modern mathematics having experienced a most impressive development in recent years. A caterpillar is a graph which reduces to a path called spine after. A lobster graph, lobster tree, or simply lobster, is a tree having the property that the removal of leaf nodes leaves a caterpillar. Hypergraphs, fractional matching, fractional coloring.