Characterizations of Non-Singular Cycles, Path and Trees

Supot Sookyang, Srichan Arworn, Piotr Wojtylak

Abstract

A simple graph is said to be non-singular if its adjacency matrix is non-singular. In this paper, we find the characterization of non-singular cycles and trees. Main Theorems: 1. A cycle $C_n$ of n points is non-singular if and only if n is not divided by 4.2. A path $P_n$ is non-singular if and only if n is even.3. A tree T is non-singular if and only if T has an even number of points and contains a sesquivalent spanning subgraph.