邢唷 > ? ^ ` ? [ \ ] € € € 欹 ` 鳵 | bjbj鎳鎳 % 勴 勴 N0 A ^ ^ ^ ^ 4 * 炳 炳 炳 h ? 6C * 蜟 . 蠿 蠿 蠿 L_ 謅 抌 ` 椯 欃 欃 欃 欃 欃 欃 $ h ^ 劫 ^ , e T^ H_ 鷉 L Fh 劫 ^ ^ 蠿 蠿 乌 竾 竾 竾 頷 ` ^ 蠿 ^ 蠿 椯 竾 e 椯 竾 竾 嵡 4 ^ ^ 蠿 翪 鄪玫笋 炳 N b 辽 > S D 溱 0 p 皝 p | " p v + ( 騜 > 0c , 竾 \c $ €c 騜 騜 騜 劫 劫 瑑 騜 騜 騜 e e e e * * * d# ? $ * * * ? * * * ^ ^ ^ ^ ^ ^ ,g 褃 u 誯 N 簨 噀b 緥 3u鲖f[隭f[MO 簨噀槝顅 剉v樄ph鱏 \O€覻T X X X NNT饄 pef[N擽(upef[ c黐Ye^ X X 2 0 1 5 t^6 g f[ u ~{W[ f[ 鱏5 0 6 0 3 5 2 0 4 1 簨噀T{錯g2 0 1 5 t^x gx x 錯 c 黐 Ye ^ ~{W[ 顅 U_ T O C \ o " 1 - 3 " \ h \ z \ u H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 3 9 5 " Xd亯 P A G E R E F _ T o c 2 3 0 0 1 4 3 9 5 \ h 1 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 3 9 8 " A b s t r a c t P A G E R E F _ T o c 2 3 0 0 1 4 3 9 8 \ h 1 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 3 9 9 " 1 . 陗簨 2 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 4 0 0 " 1 . 1 虁of孴鶺,g俰鮛 2 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 4 0 1 " 1 . 2 騗 g鴙sQ觺済 4 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 4 0 2 " 2 . 萒芠?`孴剉N o - h o l e L ( 2 , 1 ) - h鱏 5 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 4 0 3 " 2 . 1 e堽V剉萒芠?` 6 2 . 2 E M B E D E q u a t i o n . 3 剉 7 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 4 1 7 " 3 . 剉L ( 3 , 2 , 1 ) - h鱏 1 5 3 . 1 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 4 1 8 " 飴孴W剉L ( 3 , 2 , 1 ) - h鱏pe 1 5 3 . 2 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 4 1 9 " h剉L ( 3 , 2 , 1 ) - h鱏pe 2 0 3 . 3 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 4 2 0 " N,傼V剉L ( 3 , 2 , 1 ) - h鱏pe 2 1 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 4 2 2 " 耂€噀.s 2 3 H Y P E R L I N K \ l " _ T o c 2 3 0 0 1 4 4 2 3 " 魜" 2 4 剉v樄ph鱏 Xd亯 賬歔 N*N鄀T E M B E D E q u a t i o n . 3 E M B E D E q u a t i o n . 3 剉 N*N E M B E D E q u a t i o n . 3 h鱏/fc蜰vQv樄p茤 E M B E D E q u a t i o n . 3 0R^峵epe茤剉 N*N f\ E M B E D E q u a t i o n . 3 醤硩 E M B E D E q u a t i o n . 3 E M B E D E q u a t i o n . 3 購虘 E M B E D E q u a t i o n . 3 h圍y E M B E D E q u a t i o n . 3 孴 E M B E D E q u a t i o n . 3 KN魰剉輱粂sS E M B E D E q u a t i o n . 3 孴 E M B E D E q u a t i o n . 3 KN魰 g韜飴剉暒^0鍌 N*N E M B E D E q u a t i o n . 3 h鱏-N剉@b gh鱏龕N厤菑tepe E M B E D E q u a t i o n . 3 R饄KN:N E M B E D E q u a t i o n . 3 E M B E D E q u a t i o n . 3 h鱏0 E M B E D E q u a t i o n . 3 剉 E M B E D E q u a t i o n . 3 h鱏pe皨\O E M B E D E q u a t i o n . 3 /fO梍 E M B E D E q u a t i o n . 3 X[(W E M B E D E q u a t i o n . 3 E M B E D E q u a t i o n . 3 h鱏剉 g\tepe E M B E D E q u a t i o n . 3 0,g噀xvz哊 N汵{|剉 E M B E D E q u a t i o n . 3 h鱏pe賬鶴哊鍕耂pe剉 N汵 NLu0dkY,g噀貜xvz哊 E M B E D E q u a t i o n . 3 h鱏剉 N蛓豐b_剉 E M B E D E q u a t i o n . 3 h鱏顣槝0 sQ.曂 憳噑緥n顣槝 E M B E D E q u a t i o n . 3 h鱏 E M B E D E q u a t i o n . 3 h鱏萒芠橚V V e r t e x L a b e l i n g s o n G r a p h s A b s t r a c t : F o r a g i v e n g r a p h E M B E D E q u a t i o n . 3 , a n E M B E D E q u a t i o n . 3 l a b e ling is defined as a function EMBED Equation.3 : EMBED Equation.3 such that: EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 where EMBED Equation.3 denotes the distance between EMBED Equation.3 and EMBED Equation.3 . A EMBED Equation.3 is an EMBED Equation.3 l a b e l i n g s u c h t h a t n o l a b e l i s g r e a t e r t h a n E M B E D E q u a t i o n . 3 . T h e E M B E D E q u a t i o n . 3 l a b e l i n g n u m b e r o f E M B E D E q u a t i o n . 3 , d e n o t e d b y E M B E D E q u a t i o n . 3 , i s t h e s m a l l e s t n u m b e r E M B E D E q u a t i o n . 3 s u c h t h a t E M B E D E q u a t i o n . 3 has a EMBED Equation.3. The EMBED Equation.3 labeling numbers of some classes of graphs are investigated and some upper bounds about this parameter are given. Moreover, as a transmogrification, theEMBED Equation.3labeling problem are also studied here. Key words: Channel assignment problem; EMBED Equation.3 labeling; EMBED Equation.3 labeling; Hamiltonian graph1 陗 簨 1 7 3 6 t^/f簨剉CQt^(W購 Nt^E u l e r 銐砆哊 N*NS_鰁餠裛篘霳剉WT顣槝 K n i g s b e r g Neh顣槝蜰€O諲b:N簨孴觔Qbf[R薡篘0S_鰁剉pef[Luv^ g鵞E u l e r 銐砆Neh顣槝剉aIN g硩Y剉茓u髞臢臢茐vQ:N N*Npef[8nb€騗0簨迡uT g蔛鰁穬梍硩Y剉裇U\魐0R1 9 3 6 t^SYr)Rpef[禰K n i g 鶴Hr 0 gP桛VN鄀P桛Vt簨0購/f簨剉,{ N钀NW僛;`觺哊簨2 0 0 t^eg剉b済0蜰dk簨蹚eQ裇U\N亃4x剉隷f廠0蟸菑JS*NYN獈剉裇U\皊騗b:Npef[褃f[剉 N*N靣藌剉蛻亯f[褃僛剉R/e坃Y俌簨梴誰簨乬