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The minimum leaf number ml(G) of a connected graph G is the smallest number of tree leaves in any of its spanning trees. (The corresponding largest number of leaves is known ...

A tree is planted at each lattice point in a circular orchard which has center at the origin and radius r. If the radius of trees exceeds 1/r units, one is unable to see out ...

An alkane graph is a tree in which vertices correspond to atoms and edges to carbon-carbon or hydrogen-carbon bonds in a chemical alkane. In chemistry, an alkane is an ...

Consider a broadcast scheme on a connected graph from an originator vertex v in a graph G consisting of a sequence of parallel calls starting from v. In each time step, every ...

The n-centipede graph, n-centipede tree, n-comb graph (Seoud and Youssef 2017), or simply "n-centipede," is the tree on 2n nodes obtained by joining the bottoms of n copies ...

A spider graph, spider tree, or simply "spider," is a tree with one vertex of degree at least 3 and all others with degree at most 2. The numbers of spiders on n=1, 2, ... ...

A cactus graph, sometimes also called a cactus tree, a mixed Husimi tree, or a polygonal cactus with bridges, is a connected graph in which any two graph cycles have no edge ...

A problem asking for the shortest tour of a graph which visits each edge at least once (Kwan 1962; Skiena 1990, p. 194). For an Eulerian graph, an Eulerian cycle is the ...

A search algorithm of a tree that explores the first child of a node before visiting its siblings. Tarjan (1972) and Hopcroft and Tarjan (1973) showed that depth-first search ...

There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...