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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 ...

The (m,n)-tadpole graph, also called a dragon graph (Truszczyński 1984) or kite graph (Kim and Park 2006), is the graph obtained by joining a cycle graph C_m to a path graph ...

Two integers (m,n) form a super unitary amicable pair if sigma^*(sigma^*(m))=sigma^*(sigma^*(n))=m+n, where sigma^*(n) is the unitary divisor function. The first few pairs ...

The edge set of a graph is simply a set of all edges of the graph. The cardinality of the edge set for a given graph g is known as the edge count of g. The edge set for a ...

An edge cover is a subset of edges defined similarly to the vertex cover (Skiena 1990, p. 219), namely a collection of graph edges such that the union of edge endpoints ...

A graceful permutation sigma on n letters is a permutation such that {|sigma(i)-sigma(i+1)|:i=1,2,...,n-1}={1,2,...,n-1}. For example, there are four graceful permutations on ...

The edge connectivity, also called the line connectivity, of a graph is the minimum number of edges lambda(G) whose deletion from a graph G disconnects G. In other words, it ...

An graph edge of a graph is separating if a path from a point A to a point B must pass over it. Separating graph edges can therefore be viewed as either bridges or dead ends.

An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring ...

A polyhedral graph corresponding to the skeleton of a Platonic solid. The five platonic graphs, the tetrahedral graph, cubical graph, octahedral graph, dodecahedral graph, ...