The following describes the figure "Santa House" graph theoretically: "In English, the "House of NAME_1" is a popular drawing puzzle where one has to draw the house with a single continuous stroke without lifting the pen or retracing any line. Graph theoretically, this puzzle can be described as an undirected graph with the following properties:

Vertices (nodes): The house can be represented as a graph with 9 vertices, corresponding to the key points in the drawing: the roof's top, the two bottom corners of the roof, the two top corners of the house, the two bottom corners of the house, and the two intersections where the crossed lines meet in the middle of the house.

Edges: There are 8 edges connecting these vertices, representing the lines drawn in the puzzle. Specifically:
a. The roof's top is connected to both bottom corners of the roof.
b. Each bottom corner of the roof is connected to the top corner of the house on the same side.
c. Each top corner of the house is connected to the bottom corner of the house on the same side.
d. Each top corner of the house is connected to the opposite bottom corner of the house, forming a cross.
e. The two intersections in the middle of the house are connected.

Eulerian graph: The House of NAME_1 can be considered an Eulerian graph because it has an Eulerian circuit, which is a closed walk that visits every edge exactly once. The graph has four vertices with odd degree (3) and the remaining vertices with even degree (2). According to the necessary conditions  Provide your response in exactly 2 paragraphs (separated nearby paragraphs with 3 aterisk symbols ***).
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