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The conical spiral with angular frequency a on a cone of height h and radius r is a space curve given by the parametric equations x = (h-z)/hrcos(az) (1) y = (h-z)/hrsin(az) ...

A Cayley tree is a tree in which each non-leaf graph vertex has a constant number of branches n is called an n-Cayley tree. 2-Cayley trees are path graphs. The unique ...

A Cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension). The condition for three general Cevians from the three ...

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 ...

A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...

For a connected graph G of graph diameter d, the distance-k graph G_k for k=1, ..., d is a graph with the same vertex set and having edge set consisting of the pairs of ...

The first Zagreb index for a graph with vertex count n and vertex degrees d_i for i=1, ..., n is defined by Z_1=sum_(i=1)^nd_i^2. The notations Z_1 (e.g., Lin et al. 2023) ...

The half-altitude triangle DeltaA^'B^'C^' of a reference triangle DeltaABC is defined by letting A^' be the midpoint between vertex A and the foot of the A-altitude on side ...

The Laplacian spectral ratio R_L(G) of a connected graph G is defined as the ratio of its Laplacian spectral radius to its algebraic connectivity. If a connected graph of ...

The longest path problem asks to find a path of maximum length in a given graph. The problem is NP-complete, but there exists an efficient dynamic programming solution for ...