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The wreath graph W(n,k) is the graph obtained by taking n collections of k nodes and arranging around a circle such that all nodes in adjacent collections are connected. ...

The n-ladder graph can be defined as L_n=P_2 square P_n, where P_n is a path graph (Hosoya and Harary 1993; Noy and Ribó 2004, Fig. 1). It is therefore equivalent to the 2×n ...

The square of a graph is defined as its second graph power. The square of any biconnected graph is Hamiltonian (Fleischner 1974, Skiena 1990, p. 231). Mukhopadhyay (1967) has ...

Many authors (e.g., Mendelson 1963; Pervin 1964) use the term arcwise-connected as a synonym for pathwise-connected. Other authors (e.g., Armstrong 1983; Cullen 1968; and ...

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 chordless graph is a simple graph possessing no chords. A chordal graph (which possesses no chordless cycles) is not the same as (or converse of) a chordless graph (which ...

Given a planar graph G, a geometric dual graph and combinatorial dual graph can be defined. Whitney showed that these are equivalent (Harary 1994), so that one may speak of ...

"The" tetrahedral graph is the Platonic graph that is the unique polyhedral graph on four nodes which is also the complete graph K_4 and therefore also the wheel graph W_4. ...

The term "null graph" is used both to refer to any empty graph and to the empty graph on 0 nodes. Because of the conflicting usage, it is probably best to avoid use of the ...

A connected graph having e graph edges is said to be sequential if it is possible to label the nodes i with distinct integers f_i in {0,1,2,...,e-1} such that when graph edge ...