CAJ | 학술논문

简单图G的全染色是指对G的点和边都进行染色．称全染色为正常的如果没有相邻或关联元素染同一种颜色．简单图G=（VE）的正常全染色^称为它的邻点可区别全染色如果对任意两个相邻顶点u、v，有H（u）≠H（v），其中H（u）={（u））U{^（uw）｜uw∈E（G））而H（v）={h（u）}U{h（vx）｜vx∈E（G））．G的邻点可区别全染色所需最少颜色数称为G邻点可区别全色数，记为Xat（G）．本文考虑折叠立方体图FQn的邻点可区别全色数，证明了对任意n≥2，有Xat（FQn）=n＋3．
간단도G적전염색시지대G적점화변도진행염색．칭전염색위정상적여과몰유상린혹관련원소염동일충안색．간단도G=（VE）적정상전염색^칭위타적린점가구별전염색여과대임의량개상린정점u、v，유H（u）≠H（v），기중H（u）={（u））U{^（uw）｜uw∈E（G））이H（v）={h（u）}U{h（vx）｜vx∈E（G））．G적린점가구별전염색소수최소안색수칭위G린점가구별전색수，기위Xat（G）．본문고필절첩립방체도FQn적린점가구별전색수，증명료대임의n≥2，유Xat（FQn）=n＋3．
A total coloring of a simple graph G is a coloring of both edges and vertices. A total coloring is proper if no two adjacent or incident elements receive the same color. An adjacent vertex-distinguishing total coloring h of a simple graph G = （Y,E） is a proper total coloring of G such that H（u）≠ H（v） for any two adjacent vertices u and v, where H（u） = {h（u）} U）（h（uw）｜uw ∈ E（G）} and H（v） = {h（v）} U {h（vx）[vx ∈ E（G）}. The minimum number of colors required for an adjacent vertex-distinguishing total coloring of G is called the adjacent vertex- distinguishing total chromatic number of G and denoted by Xat（G）. In this paper, we consider the adjacent vertex-distinguishing total chromatic number of the folded hypercubes FQn and prove that Xat（FQn） = n ＋ 3 for n ≥ 2.