Abstract

In this paper the concept of cyclic distance is introduced. For $u,v \in V(G)$ of a connected graph $G$, the cyclic distance between $u$ and $v$ is defined as the minimum number of cycles to be traversed from a cycle containing $u$ to a cycle containing $v$. Using this notion, cyclic radius and cyclic diameter of a graph are defined. Cyclic distance matrix of a graph is also introduced and some of its properties are studied.

Keywords and Phrases

Cycle neighbor set, maximal cyclic component, cyclic radius, cyclic diameter, shrinked graph, cyclic distance matrix.

A.M.S. subject classification

05C12

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