#### Title

Characterizing 2-distance graphs

#### Document Type

Article

#### Publication Date

2019

#### Abstract

Let X be a finite simple graph. The 2-distance graph D_{2}(X) of X is the graph with the same vertex set as X and two vertices are adjacent if and only if their distance in X is exactly 2. A graph G is a 2-distance graph if there exists a graph X such that D_{2}(X)≅G. In this paper, we give three characterizations of 2-distance graphs, and find all graphs X such that D_{2}(X)≅kP_{2} or K_{m}∪K_{n}, where k≥2 is an integer, P_{2} is the path of order 2, and K_{m} is the complete graph of order m≥1.

#### Recommended Citation

Ching, R. P., & Garces, I. J. L. (2019). Characterizing 2-distance graphs. Asian-European Journal of Mathematics, 12(01), 1950006.