WP Image Borders makes it easy to:
To add borders around images in your posts, simply check the checkbox in the settings titled “Add borders to all images in blog posts.” This will automatically add the borders you’ve created to all images in your blog posts.
To add borders around images in specific parts of your site, you can add a comma-delimited list of CSS classes of the image containers. You can use this to add borders to images in a certain part of your site, or in addition to adding borders to all images in your blog posts.
WP Image Borders comes with the following options for you to style your image borders with:
Additionally, you can use this plugin to remove unwanted borders on images by leaving all border style options at their default values.
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wp-image-borders
Free Plugin