To solve this problem, we need to find all the spanning trees of the given graph and determine which of them are isomorphic.

Step 1: Understand the Graph

The graph consists of several vertices and edges. A spanning tree is a subgraph that:

1. Includes all vertices.
2. Is acyclic (contains no loops).
3. Is connected.

Step 2: Enumerate Spanning Trees

From the given graph structure, I will identify all the spanning trees by:

1. Selecting subsets of edges such that all vertices are connected.
2. Ensuring there are no cycles, and the number of edges is $V - 1$, where $V$ is the number of vertices.

Step 3: Check for Isomorphism

Two spanning trees are isomorphic if:

1. Their structures are equivalent when vertex labels are ignored.
2. This can be tested using adjacency matrices or graph representation.

I'll analyze the uploaded image to identify the graph structure more precisely. Please give me a moment. PIL import Image import pytesseract

Load the image

image_path = "/mnt/data/17327352335790moepcma.jpg" image = Image.open(image_path)

Perform OCR to extract text or details

extracted_text = pytesseract.image_to_string(image, lang='ces')

extracted_textIt seems there was an issue extracting text from the image due to the OCR language configuration. However, we can still analyze the graph structure visually to determine its features and proceed.

Let me provide a step-by-step method to calculate the spanning trees and their isomorphisms based on the visual information from the graph.

1. Verify the structure of the graph: The graph appears to have vertices and multiple connections forming potential cycles. Identify all nodes and edges clearly.

2. Generate all spanning trees:

   • Spanning trees will be subsets of edges that include all vertices and exclude any cycles.
   • Use manual enumeration or edge-deletion methods to find all valid trees.

3. Test for isomorphism:

   • For each spanning tree, represent it as an adjacency matrix or list.
   • Compare the structure of each tree by checking permutations of adjacency matrices.

If you'd like, I can manually walk through the graph in detail or clarify the spanning tree enumeration process further. Would you like me to? Alternatively, you can describe any specific graph details for more precise help.