Proving that the effective resistance across an edge in Kn is 2/n.

  1. Show that the effective resistance across an edge in Kn is 2/n .
  2. Show same thing for two vertices of the complete bipartite graph Kn,m, both of which are in the “right part” with m vertices.

This question was on my Graph Theory final and I wanted to know how to solve it.

I was considering using a theorem from Bollobas’s Modern Graph Theory book from chapter 2, but I wasn’t quite sure which one would work to give me the simplest solution..

Any help would be greatly appreciated!

Magical attacks and overcoming damage resistance

I got hit with an argument from one of my players the other day, and it goes like this:

He is playing a Monk and his unarmed attacks count as magical attacks. He was trying to punch a Web. I told him his bludgeoning attacks did no damage since it was immune to bludgeoning damage. My party disagreed with me, on the basis that his unarmed attacks are magical.

My question to this group is… In cases like fighting a werewolf it says ‘resistance bludgeoning from non-magical attacks’ but other creatures in the game it just say it is ‘resistant to bludgeoning’.

Do magical weapons and attacks cancel out the resistance if it does not specifically say so?
Or
Are these creatures resistance or immune to that damage type regardless of the weapon used?

Would the Life Transference spell be unbalanced if it ignored resistance and immunity?

I want to create a Abjuration wizard (PHB, p. 115-116) that uses the Life Transference spell (XGtE, p. 160) and the Arcane Ward feature to heal people, but I’ve heard people saying Life Transference is bad due to how it interacts with resistance (half the damage taken = half the healing).

That is pretty relevant for me, because of the Spell Resistance feature that Abjuration wizards get at 14th level.

What if Life Transference worked like the Overchannel feature from the School of Evocation wizard (PHB, p. 118): necrotic damage that ignores resistance and immunity?

I believe that would be very thematically appropriate considering the fact that it is a self-sacrifice spell. I know that this is all up to the DM, but I want to know: Would that be unbalanced? Could that somehow be exploited?

Can someone with vulnerability to necrotic damage benefit from resistance, in regards to the Evocation wizard’s Overchannel feature?

Overchannel (Evocation Wizard feature) states that the necrotic damage it deals ignores immunities or resistances to its damage – but something like vulnerabilities would still be applied.

If I am vulnerable to necrotic damage, then gain resistance to necrotic damage, do I:

  • Receive normal damage from Overchannel as the two void each other?
  • Ignore my resistance and deal double damage from being vulnerable?

Does the Appartus of Kwalish have resistance to all damage?

The Apparatus of Kwalish includes in it’s description the following statistics:

Armor Class: 20
Hit Points: 200
Speed: 30 ft., swim 30 ft. (or 0 ft. for both if the legs and tail aren’t extended)
Damage Immunities: poison, psychic

However, according to Magic Item Resilience (DMG p.141):

Most magic items are objects of extraordinary artisanship, assembled from the finest materials with meticulous attention to detail. Thanks to this combination of careful crafting and magical reinforcement, a magic item is at least as durable as a regular item of its kind. Most magic items, other than potions and scrolls, have resistance to all damage. Artifacts are practically indestructible, requiring extreme measures to destroy.

Is the Apparatus of Kwalish resistant to all damage by virtue of being a magic item or is the general rule overridden because the Apparatus’ statistics do not mention any resistances?

What if a revenant (monster) gains fire resistance?

As a GM, I use some revenants for my campaign. Those revenants all have class abilities and 2 are spell casters (an abjuration mage and alchemist artificer). The “problem” (it’s not a problem, but an “and what if they do that?”) is that they can use the Protection from Energy spell, so they can have fire resistance.

My question is: What happens if they gain fire resistance (or radiant resistance)? Do you think they lose their regeneration weakness (that doesn’t work when fire damage is dealt)?

What is, or should be, the Magic Resistance required to resist the Fuse spell?

The Fuse spell states, in its Added Effects block, +5 to the MR and +5 to the maximum Presence affected. However, nowhere in the text I have in front of me (taken from the basic sourcebook in English) is the base MR stated – only the base Presence. The text is included below.

Unites two beings in a single body, creating a new individual who possesses the characteristics and abilities of both. The caster designates which capacities prevail, selecting those that he is interested in from each. If the spell joins a fighter and a psychic, for example, the resulting individual could have the fighting ability of the warrior, the mental powers of the mentalist, and the highest Secondary Abilities of each one. Control of the resulting united body falls to whichever of the two wins an Opposed Check of Willpower, although some characteristics typical of the other personality can be retained. The original bodies remain in the state they were in before the fusion and so, when the spell lapses, return to the state and condition they were in before it was cast. The death of the joint entity causes the death of both original people. The total Presence of both originals cannot be more than 80. It is also possible to Fuse an individual with objects, in which case the GM can award the result the advantages and abilities he considers appropriate.

What is the base MR of the Fuse spell? If no canonical source exists, what should the base MR be?

Can I have two different Resistance boon active at the same time?

This is the scenario:

  • Round 1: invoke Resistance Precise
  • Round 2: invoke Resistance Forceful, don’t sustain Resistance Precise

If you have a boon in effect and do not sustain it, the boon ends when your turn is over.

During round 2, Resistance Precise is still active until the end of my turn, together with Resistance Forceful. But the rule says

While targets may be effected by different boons, you may not stack the same boon multiple times; if a second invocation of a boon would affect a character, they choose which boon to keep and which one to negate.

Does this mean that I can’t have two different Resistance boon active?

Resistance and Parry

I am running a barbariand fighter multiclass. When raging, I have resistance to all damage but physic. And the fighter maneuver parry allows me to expend a superiority die to reduce damage. it is unclear when these would trigger. Rage Half it then battle master die it lower? Or Battle master die then rage half it? I dont believe it is stacking resistances because the battle mater ability is not a resistance.