Abstract
We apply the concept of
m
-polar fuzzy sets to graph structures. We introduce certain concepts in
m
-polar fuzzy graph structures, including strong
m
-polar fuzzy graph structure,
m
-polar fuzzy
D
i
-cycle,
m
-polar fuzzy
D
i
-tree,
m
-polar fuzzy
D
i
-cut vertex, and
m
-polar fuzzy
D
i
-bridge, and we illustrate these concepts by several examples. We present the notions of
ϕ
-complement of an
m
-polar fuzzy graph structure and self-complementary, strong self-complementary, totally strong self-complementary
m
-polar fuzzy graph structures, and we investigate some of their properties.