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/* These styles are specific to my theme. You will want to adjust them for your own theme: */
/* essentially remove any link styling from the text, but add it back to the excerpt's link. */
.home .entry-content a,
.archive .entry-content a {
	color: #333;
	text-decoration: none;
}

.home .entry-content .read-more,
.home .entry-content .more-link,
.archive .entry-content .read-more,
.archive .entry-content .more-link {
	color: #aaa;
	text-decoration: underline;
}

<?php 

/* add link at beginning of excerpt */
add_filter( 'genesis_entry_content' , 'lgd_clickable_open', 1 );
function lgd_clickable_open() {
     if (is_home() || is_front_page() || is_archive() ) {
          printf( '<a href="%s" alt="%s">', get_permalink(), the_title_attribute( 'echo=0' ) );
     }
}

/* end link at end of excerpt */
add_filter( 'genesis_entry_content' , 'lgd_clickable_close', 11 );
function lgd_clickable_close() {
     if (is_home() || is_front_page() || is_archive() ) {
          printf( '</a>' );
     }
}