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Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...

A regular polygram {n/k} is generalization of a (regular) polygon on n sides (i.e., an n-gon) obtained by connecting every ith vertex around a circle with every (i+k)th, ...

Let a graph G=(V,E) be defined on vertex set V and edge set E. Then a construction sequence (or c-sequence) for G is a linear order on V union E in which each edge appears ...

Vince and Bóna (2012) define an assembly tree T for a connected simple graph G on n nodes as a binary rooted tree with n leavesTree Leaf and n-1 internal nodes and satisfying ...

The chromatic number of a graph G is the smallest number of colors needed to color the vertices of G so that no two adjacent vertices share the same color (Skiena 1990, p. ...

In a graph G, two graph vertices are adjacent if they are joined by a graph edge.

A graph vertex in a graph is said to be an even node if its vertex degree is even.

Bonato et al. (2014, 2015) defined the burning number of a simple graph as follows. Consider a process called burning involving are discrete time steps. Each node is either ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

A self-avoiding polygon containing three corners of its minimal bounding rectangle. The anisotropic area and perimeter generating function G(x,y) and partial generating ...