Here is an example CR 13 Dragon. This Dragon can probably take any 20th level character in a 1 on 1 fight. So, short of an epic character or a deity, this Dragon is not going to be afraid of any single PC. The Dragon would know, though, that a group can be more dangerous than an individual enemy. On the other hand, groups of enemies is why the Dragon has a breath weapon.
young adult red dragon; CR 13; Huge dragon (fire); HD 19d12+95 (218 hp); Init +4; Spd 40 ft., fly 150 ft. (poor); AC 26, touch 8, flat-footed 26; BAB +19; Grapple +37; Atk +27 melee (2d8+10, bite) or +27 melee (2d8+15, crush); Full Atk +27 melee (2d8+10, bite) and +25 melee (2d6+5, 2 claws) and +25 melee (1d8+5, 2 wings) and +25 melee (2d6+15, tail slap); or +27 melee (2d8+15, crush); SA Breath weapon, crush, frightful presence, spells; SQ Blindsense 60 ft., darkvision 120 ft., DR 5/magic, immunity to fire, sleep, and paralysis, locate object, keen senses, SR 19, vulnerability to cold; Space/Reach 15/10 (15 with bite); AL CE; SV Fort +16, Ref +11, Will +13; Str 31, Dex 10, Con 21, Int 14, Wis 15, Cha 14.
Skills and Feats: Bluff +21, Concentration +24, Diplomacy +23, Intimidate +4, Jump +35, Knowledge (religion) +21, Listen +21, Search +21, Spellcraft +13, Spot +21; Ability Focus (breath weapon), Flyby Attack, Improved Initiative, Improved Sunder, Multiattack, Power Attack, Wingover.
Breath Weapon (Su): 50 ft. cone of fire, 10d10 points of fire damage, Ref save DC 26 half.
Frightful Presence (Ex): 150 ft. range; creatures must succeed at a Will save (DC 21) or become panicked for 4d6 rounds (if 4 or less HD) or become shaken for 4d6 rounds (5 HD or more).
Crush (Ex): This special attack allows a flying or jumping dragon of at least Huge size to land on opponents as a standard action, using its whole body to crush them. Crush attacks are effective only against opponents three or more size categories smaller than the dragon (though it can attempt normal overrun or grapple attacks against larger opponents). A crush attack affects as many creatures as can fit under the dragon’s body. Creatures in the affected area must succeed on a Reflex save (DC 24) or be pinned, automatically taking bludgeoning damage during the next round unless the dragon moves off them. If the dragon chooses to maintain the pin, treat it as a normal grapple attack. Pinned opponents take damage from the crush each round if they don’t escape. Crush attack deals 2d8+15 points of damage.
Keen Senses (Ex): Sees four times as well a human in shadowy illumination and twice as well in normal light. also has darkvision out to 120 ft.
Locate Object (Sp): 5/day (as Sor5).
Spells Known (6/7/5; base DC = 12 + spell level): 0--arcane mark, detect magic, ghost sound, mage hand, open/close, read magic; 1--alarm, cure light wounds, mage armor, true strike; 2--cure moderate wounds, invisibility