Which of the following graphs is isomorphic to

To check graph isomorphism between the given graph $G$ and the options, we examine the structural invariants:

1. Vertex and Edge Count:

   • The given graph has $7$ vertices and $7$ edges.

2. Degree Sequence:

   • The given graph consists of a $5$-cycle with one vertex connected to $2$ pendant vertices (degree $1$).

   • The degrees of the vertices are: one vertex of degree $4$, four vertices of degree $2$ (forming a $5$-cycle with the degree-$4$ vertex), and two vertices of degree $1$.

   • Degree sequence: $(4, 2, 2, 2, 2, 1, 1)$.

3. Analyzing Option (B):

   • Option (B) contains $7$ vertices and $7$ edges.

   • The central vertex has degree $4$.

   • It is adjacent to two vertices of degree $1$ (pendants) and two vertices of degree $2$ that are part of a $5$-cycle.

   • Hence, graph (B) is isomorphic to the given graph.