diff --git a/R/structural-properties.R b/R/structural-properties.R
index 71f8bc54bbe..e506457f407 100644
--- a/R/structural-properties.R
+++ b/R/structural-properties.R
@@ -2800,6 +2800,8 @@ bfs <- function(
   }
   if (parent) {
     res$parent <- res$parent + 1
+    # Convert 0 (no parent) to NA
+    res$parent[res$parent == 0] <- NA
   }
   if (pred) {
     res$pred <- res$pred + 1
@@ -2812,9 +2814,6 @@ bfs <- function(
     if (order) {
       res$order <- V(graph)[.env$res$order, na_ok = TRUE]
     }
-    if (parent) {
-      res$parent <- create_vs(graph, res$parent, na_ok = TRUE)
-    }
     if (pred) {
       res$pred <- create_vs(graph, res$pred, na_ok = TRUE)
     }
@@ -3053,6 +3052,8 @@ dfs <- function(
   }
   if (parent) {
     res$parent <- res$parent + 1
+    # Convert 0 (no parent) to NA
+    res$parent[res$parent == 0] <- NA
   }
 
   if (igraph_opt("return.vs.es")) {
@@ -3062,7 +3063,6 @@ dfs <- function(
     if (order.out) {
       res$order.out <- V(graph)[.env$res$order.out, na_ok = TRUE]
     }
-    if (parent) res$parent <- create_vs(graph, res$parent, na_ok = TRUE)
   } else {
     if (order) {
       res$order <- res$order[res$order != 0]
diff --git a/man/make_circulant.Rd b/man/make_circulant.Rd
index 50928495616..f3d3afcb949 100644
--- a/man/make_circulant.Rd
+++ b/man/make_circulant.Rd
@@ -49,10 +49,12 @@ Other deterministic constructors:
 \code{\link{make_empty_graph}()},
 \code{\link{make_full_citation_graph}()},
 \code{\link{make_full_graph}()},
+\code{\link{make_full_multipartite}()},
 \code{\link{make_graph}()},
 \code{\link{make_lattice}()},
 \code{\link{make_ring}()},
 \code{\link{make_star}()},
-\code{\link{make_tree}()}
+\code{\link{make_tree}()},
+\code{\link{make_turan}()}
 }
 \concept{deterministic constructors}
diff --git a/man/make_full_multipartite.Rd b/man/make_full_multipartite.Rd
index 04c9a1ea840..e0cedcb7102 100644
--- a/man/make_full_multipartite.Rd
+++ b/man/make_full_multipartite.Rd
@@ -48,6 +48,7 @@ Other deterministic constructors:
 \code{\link{graph_from_literal}()},
 \code{\link{make_}()},
 \code{\link{make_chordal_ring}()},
+\code{\link{make_circulant}()},
 \code{\link{make_empty_graph}()},
 \code{\link{make_full_citation_graph}()},
 \code{\link{make_full_graph}()},
diff --git a/man/make_turan.Rd b/man/make_turan.Rd
index 3eec18e4487..6431e0f76ba 100644
--- a/man/make_turan.Rd
+++ b/man/make_turan.Rd
@@ -47,6 +47,7 @@ Other deterministic constructors:
 \code{\link{graph_from_literal}()},
 \code{\link{make_}()},
 \code{\link{make_chordal_ring}()},
+\code{\link{make_circulant}()},
 \code{\link{make_empty_graph}()},
 \code{\link{make_full_citation_graph}()},
 \code{\link{make_full_graph}()},
diff --git a/tests/testthat/_snaps/structural-properties.md b/tests/testthat/_snaps/structural-properties.md
index e006e10afcb..89e93366bc5 100644
--- a/tests/testthat/_snaps/structural-properties.md
+++ b/tests/testthat/_snaps/structural-properties.md
@@ -29,9 +29,8 @@
       0 1 2 0 0 
       
       $parent
-      + 5/5 vertices, named:
-         a    b    c    z    d 
-      <NA> <NA>    b <NA> <NA> 
+       a  b  c  z  d 
+      -1 NA  2 -1 -1 
       
       $pred
       + 5/5 vertices, named:
@@ -51,9 +50,8 @@
       [1] "out"
       
       $father
-      + 5/5 vertices, named:
-         a    b    c    z    d 
-      <NA> <NA>    b <NA> <NA> 
+       a  b  c  z  d 
+      -1 NA  2 -1 -1 
       
 
 # bfs() deprecated arguments
diff --git a/tests/testthat/test-structural-properties.R b/tests/testthat/test-structural-properties.R
index 422e615f969..6709157e8db 100644
--- a/tests/testthat/test-structural-properties.R
+++ b/tests/testthat/test-structural-properties.R
@@ -259,6 +259,52 @@ test_that("bfs() does not pad order", {
   expect_equal(as.numeric(bfs(g, root = 2, unreachable = FALSE)$order), c(2, 1))
 })
 
+test_that("bfs() parent is numeric vector with NA, not igraph.vs", {
+  # Verify fix for https://github.com/igraph/rigraph/issues/1576
+  g <- sample_gnm(10, 20)
+  res <- bfs(g, 1, parent = TRUE)$parent
+  
+  # parent should be a numeric vector, not igraph.vs
+  expect_true(is.numeric(res))
+  expect_false(inherits(res, "igraph.vs"))
+  
+  # str() should work without error
+  expect_no_error(str(res))
+  
+  # Indexing should work without error
+  expect_no_error(res[1])
+  
+  # Root vertex should have NA parent
+  expect_true(is.na(res[1]))
+  
+  # Other vertices should have numeric parents (or -1 for unreachable)
+  non_root <- res[-1]
+  expect_true(all(is.na(non_root) | non_root > 0 | non_root == -1))
+})
+
+test_that("dfs() parent is numeric vector with NA, not igraph.vs", {
+  # Verify fix for https://github.com/igraph/rigraph/issues/1576
+  g <- sample_gnm(10, 20)
+  res <- dfs(g, 1, parent = TRUE)$parent
+  
+  # parent should be a numeric vector, not igraph.vs
+  expect_true(is.numeric(res))
+  expect_false(inherits(res, "igraph.vs"))
+  
+  # str() should work without error
+  expect_no_error(str(res))
+  
+  # Indexing should work without error
+  expect_no_error(res[1])
+  
+  # Root vertex should have NA parent
+  expect_true(is.na(res[1]))
+  
+  # Other vertices should have numeric parents (or -1 for unreachable)
+  non_root <- res[-1]
+  expect_true(all(is.na(non_root) | non_root > 0 | non_root == -1))
+})
+
 test_that("diameter() works -- undirected", {
   g <- largest_component(sample_gnp(30, 3 / 30))
   sp <- distances(g)