This paper investigates the effect of charge on traversable wormhole (WH) geometry in the context of $f(\mathcal{G})$ theory, where $\mathcal{G}$ is the Gauss-Bonnet term. The authors use the embedding class-I technique to develop a shape function for a static spherical spacetime with anisotropic matter configuration. They construct a wormhole geometry that satisfies all the required constraints and connects asymptotically flat regions of the spacetime. The behavior of energy conditions for various models of the theory is analyzed to determine the existence of viable traversable WH solutions. The study reveals that viable traversable WH solutions exist in this modified theory. The paper also discusses the Karmarkar condition, which is used to develop the shape function, and the induced-matter theory, which extends the concept of Kaluza-Klein theory to incorporate matter into the embedding process. The authors analyze the field equations and the behavior of energy conditions for different models of $f(\mathcal{G})$ gravity, showing that the null, dominant, weak, and strong energy conditions are violated for some parameter values. However, they find that viable traversable WH structures can be obtained for specific parametric values. The paper concludes by summarizing the findings and discussing the implications for understanding WHs in modified gravitational theories.This paper investigates the effect of charge on traversable wormhole (WH) geometry in the context of $f(\mathcal{G})$ theory, where $\mathcal{G}$ is the Gauss-Bonnet term. The authors use the embedding class-I technique to develop a shape function for a static spherical spacetime with anisotropic matter configuration. They construct a wormhole geometry that satisfies all the required constraints and connects asymptotically flat regions of the spacetime. The behavior of energy conditions for various models of the theory is analyzed to determine the existence of viable traversable WH solutions. The study reveals that viable traversable WH solutions exist in this modified theory. The paper also discusses the Karmarkar condition, which is used to develop the shape function, and the induced-matter theory, which extends the concept of Kaluza-Klein theory to incorporate matter into the embedding process. The authors analyze the field equations and the behavior of energy conditions for different models of $f(\mathcal{G})$ gravity, showing that the null, dominant, weak, and strong energy conditions are violated for some parameter values. However, they find that viable traversable WH structures can be obtained for specific parametric values. The paper concludes by summarizing the findings and discussing the implications for understanding WHs in modified gravitational theories.