The elements which exhibit both vertical and horizontal similarities are:

Options

A. inert gas elements
B. representative elements
C. transition elements
D. none of these

Explanation

To solve the question "The elements which exhibit both vertical and horizontal similarities are:", we can follow these steps:

### Step-by-Step Solution:

**Step 1: Understand the Question**
- The question asks for elements that show similarities both vertically (within a group) and horizontally (across a period) in the periodic table.

**Step 2: Identify the Relevant Groups**
- The elements that typically show such similarities are the transition metals, which are located in groups 3 to 12 of the periodic table.

**Step 3: Characteristics of Transition Metals**
- Transition metals have partially filled d orbitals. This unique electronic configuration allows them to exhibit similar properties both vertically and horizontally.

**Step 4: Analyze Vertical Similarities**
- Vertically, as you move down a group of transition metals, the atomic size increases, but the properties remain similar due to the filling of d orbitals and the lanthanoid contraction, which minimizes the expected increase in size.

**Step 5: Analyze Horizontal Similarities**
- Horizontally, as you move across a period from left to right, the atomic size generally decreases due to an increase in effective nuclear charge. However, transition metals maintain similar properties due to their electronic configurations.

**Step 6: Conclusion**
- Based on the above analysis, we conclude that the elements that exhibit both vertical and horizontal similarities are the transition elements.

**Final Answer:**
- The correct answer is the transition elements (groups 3 to 12).