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A weighted adjacency matrix A_f of a simple graph is defined for a real positive symmetric function f(d_i,d_j) on the vertex degrees d_i of a graph as ...

Graphs corresponding to closed walks of length k are known as k-cyclic graphs, or C_k-graphs for short. C_k-graphs are connected by definition. The numbers of C_k-graphs for ...

An acyclic digraph is a directed graph containing no directed cycles, also known as a directed acyclic graph or a "DAG." Every finite acyclic digraph has at least one node of ...

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 ...

In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle. The term is also ...

A (p,q)-graph is edge-graceful if the edges can be labeled 1 through q in such a way that the labels induced on the vertices by summing over incident edges modulo p are ...

Flower graphs are a name given in this work to the generalization of the flower snarks J_n for positive n=5, 7, 9, ... to all integer n>=5. They are illustrated above for n=5 ...

The Floyd-Warshall algorithm, also variously known as Floyd's algorithm, the Roy-Floyd algorithm, the Roy-Warshall algorithm, or the WFI algorithm, is an algorithm for ...

Guy's conjecture, which has not yet been proven or disproven, states that the graph crossing number for a complete graph K_n is ...

The Jahangir graph J_(n,m) is a kind of generalized wheel graph with consisting of mn circular vertices and a central vertex connected to every mth vertex around the circle. ...