Propriedades combinatórias e espectrais de grafos com restrição de regularidade
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(283) vxw,y4wètvxwhµ ý w m vxws\r
(284) vxw,yw"tvxwЩ
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(287) v~~}u¢H£t¡Zryxw"w,Z}*s*}*v(rr^wnann"nn"nnn"nn"nn"nnn"n¸·[ }*}*}.
(288) ©jn v(r[t^yxw²zr
(289) v~~}u¢ _w,y{Zryxww,Z}*s*}*v(rry{ £t^~v~}* _}\r
(290) }uyHnRnn"nn"nnn"nn"nn"nnn"n¸·· ©jn mv(r[t&,tãr
(291) z¥w ry)jry)}*zr
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(293) !#"%$'&. ). (. <Ê#Ñ+*=>Ï-,/.0*. þ ~v(r
(294) r
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(297) }uyry¡r
(298) ~v~}*êHw,y§w&r
(299) xr,¨ }\r¡wv(r[tyw&r0w ´j}uy~x¨ }\r¡ww,y~~v~~v(ry wºvxws\r
(300) v~}urwßry¤Zr
(301) }uy¡yxw-y(r
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(303) sutvxw,y0zvx|zv~}utyÝr ¡r
(304) ~v~}*ê-w-r
(305) xr,¨ }\rjßKrèzr
(306) v~~}*v¡ty0 r
(307) sutvxw,y^zvx|zv~}uty¡w4¡r
(308) ~v~}*êHw,y¡w-r
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(310) v(rºr¤Hr
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(313) vxw,yHߥzr
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(315) v~~}u ¢ _w,yZryxww,Z}*s*}*v(rryHn)tÓw,y~xw tj~w,~}* tß_w,y~(r
(316) ¥wsuw,,w yxw tH ryFzvxtzv~}uw,rwvxw wvxw Zxw,y)(r
(317) Zxtîw,y~~v~~v(rtyFv(r[ty),t0t&rty r
(318) sutvxw,yRw) w,xtvxw,yRzvx|zv~}uty¬ry~r¡r
(319) ~v~}*êKwKr
(320) xr,¨ }\rjßxwv~^}* r
(321) t,t2vxw w,yA,t y~}uwv(r ¢ _w,y vxw wvxw Zxw,yî&¡r
(322) ~v~}*ês\r
(323) zs\r}\r
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(325) v~}urw"vxw wv~}ury°x¨. _}* t^r&yxwvKr
(326) ^zs\r 0w Zxww,y~~rty{w,yxw"tyr
(327) ty{yxw,yxyxw Z(rt^y54,sut _}* Zxwßy~v~}* t^ t~v(r
(328) (r
(329) 0w Zxt¡w"j}* wvxy(ry Zw,y~5 _w,y{7 r 6w,tv~}\r¡ty§v(r[t9y 8Fv(r[ty,tâvxw,y~~v~}u ¢ _w,ywt^}*; :
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(331) vxw,y§C w BEDFG2HJI'FK< 6L1t µjo ß 3 wµA @gßv~z¥tywr
(332) xt0tNv My~0ty§wv(r[t y < OJ5 P·© @gß zr
(333) v~~}u ¢ _w,yryxyxt_}\rryrº¡r
(334) ~v~}*êHw,yw0zryxyxw}utRy QS< )ÃjµA @gßR,t y~~v~¢H£tèw0v(r[ty&,tð~vx¨,y r
(335) sutvxw,y zvx|zv~}ut y < OT>µ @gß_Hr
(336) v(rxwv~}*ê[r¢H£twv(r[ty),t Z¦0wvxtw{}* wz¥w ¨ }\r&Zrjv(³
(337) ~}u,t&,t Z w ´t < °r
(338) v(áA m @g߬r
(339) zs*}uHr¢H£tèw¡ ¢ _w,y&w4r
(340) xt_,tv~vxws\r¢H£t#rtJw,y~~tJT w U2VJIWBAF X5VYZDF[< !Ã 6{A @gßRv(r[tyw 3. \^]`_Nacb deJfgAfaheJfji b k^_mlnf5k^olnfL_Np i q eAdoJfb eAdi _Na^fLrtslvuWwx y{zw|n}2~}2~A^. o.
(341) N; O,Q GH
(342) 879RMS T8 U. j}uy~:
(343) }\rvxws\r
(344) v57< §t_m@gßwxn §wr,tvxt¤,t< )®§Ãj ·9@gßty{v(r[ty,tâzr
(345) v~~}u¢ _w,yw,Z}*s*}*v(rrytv(r
(346) ²}* Z~vxt_jê,}utyz¥tv"Ãjr51y w < ÃjrH©
(347) ߥÃjrH©©A@gßt w4&,t y~}uwv(rtÝt0v(r[t¤Zt_}uw Zxwn:tv54ºß r¡w,y~}* r¢H£t¤wzr
(348) v~~}u¢ _w,y w,Z}*s*}*v(rry^y~v~ wÝr
(349) z¥w ryw < Ã_5 1·[ß:å"÷ @gn ¿ yzr
(350) v~~}u ¢ _w,yw,Z}*s*}*v(rry^y~v~ ww < )ÃjµA @ ,t0t§ Hryxt§zr
(351) v~~}us\r
(352) vFryRzr
(353) v~~}u ¢ _w,yFryxyxt_}\rry¬r¡r
(354) ~v~}*êHw,y¬w°zryxyxw}utyH{n A < Ã_5 1·[ß Ãjµáß §t_mjß )®§Ãj 9· @0ty~~v(r yxwKZw°rzr
(355) v~~}*v¬ryRzr
(356) v~~}u ¢ _w,yAw,Z}*s*}*v(rry¬w°2v(r[ t 4)z¥tyxy * wstxwv }* jtv~¡r¢H£tr,wvxHrKty r
(357) sutvxw,y zvx|zv~}uty:t w,xtvxw,y zvx|zv~}uty:r°vxw,y~z¥w,~}* r)¡r
(358) ~v~}*ê)wFr
(359) xr,¨ }\r ,t vxw,vxyxt&r§ s*~}uj}*v(r[t&w{0w tv)tvxwºßjt"v(r[tZt_}uw Zxwn A zr
(360) v~~}us\r
(361) vHß_0ty~~v(r yxw Zw{t"z¥ts*}* |^}ut&Hr
(362) v(rxwv uy~~}u,t&r§¡r
(363) ~v~}*ê§wr
(364) xr,¨ }\rt"v(r[tZt_}uw Zxwj}* _}uwt"z¥ts*}* |^}ut Hr
(365) v(rxwv uy~~}u,tÒrä¡r
(366) ~v~}*êJwJr
(367) xr,¨ }\r#t#v(r[tn ç vxw,y~s*(rtÒyxw0w2s 1r
(368) ZxT w 44zvxtH rtÒw < Oäþ§µ 9 · @gßt wty,t ,w}*xtywzr
(369) v~~}u¢H£t¤w,Z}*s*}*v(rr¡w"v(r[t¡Zt_}uw Zxwy(£t¡w,y~xw j}uty§rv(r[ty ,t ,t ' Zxty-wä 4v~~}u,w,yº £ t M }*xtyHn ¿ t_¢H£tñwäv(r[t Zt_}uw Zxwät}"vxw,w,yx,t¥wv~(r w < )r
(370) z·A @t w{yxwKzvxtH r"Zw°zr
(371) v(r§ s*~}uj}*v(r[ t JßZt§z¥ts*}* |^}utHr
(372) v(rxwv~}uy~~}u,tw°¡r§¡r
(373) ~v~}*ê wr
(374) xr,¨ }\rjßjw M }ur&r§zr
(375) v~~}*v°ry)|v~}*(ry)w üTí ñ yxt¤rr,¢H£t&tv~z¥twr
(376) xt0tNv My~0ty C w Jß:j}* _}uw¤tºz¥ts*}* |^}utJHr
(377) v(rxwv uy~~}u,tJr4¡r
(378) ~v~}*êÝw¤r
(379) xr,¨ }\rºz¥w,y(rrº ë §n ¿ yzr
(380) v~~}u ¢ _w,y w,Z}*s*}*v(rry)wty¬v(r[tyFZt_}uw Zxw,y)y~v~ w.r
(381) }* rjß_w 6w,tv~}\rty°)|_j}* t y w < :··jß_ ÃjµAá @ w ,t Z~v(r yxw¡r^zvxtH r07 t 6w,tvxw¡r0 w 7su9t j-t wyxw"vxw,,tv~vxw&r^w,y~xw,y{,t ,w}*xty n ¿ s 4Ój}uyxyxtß ryzr
(382) v~~}u ¢ _w,yw,Z}*s*}*v(rry^w¤tyv(r[tyZt_}uw Zxw,yy(£t-vxw wv~}uty& tJw,y~~tèw¡v(r[ty&Zw¡x¨ ¡r¡¡r
(383) ~v~}*ê^wr
(384) xr,¨ }\rÝ,tÐtÝyxw t¡¡r
(385) }utv§ r
(386) sutv§zvx|zv~}u t ^ z¥w,Zw 't 7wÐzr
(387) v~~}us\r
(388) vHß w,y~xw,y{s*~}uj}*v(r[ty§y~v~ wâ r^,t y~~v~¢H£t¤w"¡r0,tsuw,,¢H£7 t M }*(r0wy~v(r[ty{zvxt}*}utyZw R Hr
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(390) vxw,yy~v~ wÐw< 6L1t µjo ß 3 wµA@R t¤,t Zxw ´jxtÝtyv(r[tytv~xw0w Zxw vxws\r
(391) vxw,y¬w°tyBEDFG2HJI'Fn`§tyRvxw,y~s*(rty¬rAr
(392) zvxw,yxw Z(rtyFw,y~(rHr yxw°tlrxt"w)2v(r[tvxws\r
(393) v ,tÀ,t ' Zxt íî£ïuðEñl vxws\r
(394) v&xwv î ð ,t0t4 r
(395) sutvzvx|zv~}utºr4y~rÝ¡r
(396) ~v~}*ê¡w¡r
(397) xr,¨ }\rjn )t0t4yxw& wv(³¤ tº°r
(398) 'z *~sut4ß7ty",t ' Zxty íî£ïuðEñl vxws\r
(399) vxw,y&w^ry§zr
(400) v~~}u ¢ _w,yw,Z}*s*}*v(rryw,y~(£t vxws\r}ut rty"x³JZwÝ ,t ' Zxt íî£ïuðEñl vxws\r
(401) vÝwÝv(r[tèvxws\r
(402) v0}* jê4¡rè}*zr
(403) v~~}u¢H£t w,Z}*s*}*v(rrjn þ ,t^zsuw0w Z(r
(404) vwÓv(r[t¡vxws\r
(405) ~}* r
(406) 0w Zxw0r^¡r¡zr
(407) v~~}u¢H£tÝt¤,t ' ZxtÝw 4v~~}u,w,y5 ßy~v~ w ¡m]`_Nacb deJfgsaheJfji b k^_mlnf5k^olnfL_Np i q eAdoJfb eAdi _Na^fLrtsl¢~^}£wt¤n¥m¦|^¥§¨x w|v§|cwnzA© ^ ªN]`_Nacb deJfgsLeJfi b k^_mlnf5k^olnfL_Np«i q eAdoJfLb eAdi _Na^fLrtsl`§|cwnzA©?^uZ~}£¤n© ~9§.
(408) N; O,Q GH
(409) 879RMS T8 c. r0§w,t0w~v~}\rjßr
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(411) vxw,y vxws\r
(412) ~}* r
(413) 0w Zxwrzr
(414) v~~}u ¢ _w,yKt,t ' Zxtw 4v~~}u,w,y 4(r
(415) 4.~}*s*}*ê[rr,t0t&zvxt_,w,j}*0w Zxt0w ,t y~~v~¢H£tÝw tH tyv(r[tytv~xw0w Zxw&vxws\r
(416) vxw, y < Ã_w}·A @RtJv(r[ty £t¡vxws\r
(417) vxw,y"xr^¡r
(418) ~v~}*ê wr
(419) xr,¨ }\r^xwÓm& r
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(421) zs*}uHr ¢ _w,yHn þ ~v(r
(422) r
(423) s21tr
(424) zvxw,yxw Z(rt w,y~(r§j}uyxyxwv~(r¢H£t§}* yxwvxw yxwK t",t Zxw ´jxtryA}* Zxwv(r,¢ _w,yFw Z~vxwr6w,tv~}\r ty^v(r[tyw¤r=6w,tv~}\rJry#Oèr
(425) ~v~}*êHw,yHßAy~}*~r
(426) t yxw¡ rJ³
(427) vxwHrºy~r
(428) s*0w Zxw4w,y~}* rrºz¥tv#6w,tv~}\r ¬y~z¥w,~v(r
(429) s:ty"v(r[ty ®L n §w Z~vxt¤w,y~(r¡³
(430) vxwHr0w,y~(r
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(432) ~v~}*êHw,yryxyxt_}\rryHßj,t0t^z¥tv{w ´w^zsutßr&¡r
(433) ~v~}*êwr
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(435) ~v~}*êw§}* }u¨ }\rjßjr¡r
(436) ~v~}*ê{s\r
(437) zs\r}\r
(438) rw{r§¡r
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(441) }uy¬vxws\r ¢ _w,vy 4 r
(442) ¥tvxrr§wFtv~¡rw ´jz2s u}*(rz¥tvFÃjr5 1¯y < ÃjrH©
(443) t @gßZÃ_w}uw°s < Ã_w}\©Aµ @w°åt
(444) 楡r
(445)
(446) < åt
(447) l© @gß w Z~vxwKt~vxtyHß r
(448) z¥w,y(r
(449) vKw)x³xwv{y~}ut}* }u}\rr^r
(450) Zxwv~}utv~0w ZxS w wvHßjz¥tv{w ´w^zsut±ß < )tZÃZ}\ ·!ß ²#w}\'ß 72} 1A© @ nARr v(r
(451) suws\r
(452) 0w Zxwrty°w,yxw Z ts* _}*0w Zxtyt~}uty°z¥tLv Oèr
(453) xw¡³
(454) ~}u,tyHßw ,t Z~v(r
(455) yxw" rs*}*xwv(r
(456) ~v(r&vxw w vx¨ }\ryFr§r
(457) ¥tvxr
(458) w yFw Z ts* w tw,y~z¥w,~vxty¬w°¡r
(459) ~v~}*êHw,yFryxyxt_}\rry¬r0t_wsutyAw°v(r[tyRy(rty w.t~v(ry{³
(460) vxwHryF}uw Z MHryHß,t0# t 4tHryxt&# r ³' *^}uHS r < åHmjo ßK 6·Eß ²/}*s\µ @gn 3 ry)¦s*~}*¡ry 4,Hrryt Z¦0wvxt0w"zs*}uHr ¢ _w,y{Zwr
(461) ¥tvxr
(462) Ó# ' r 6w,tv~}\7 r ¬y~z¥w,~v(r
(463) styv(r[tyKvxw,yx,wº}*xt v(r
(464) z}ur
(465) 0w Zxw¯n "r^ ry~(rs*}*xwv(r
(466) ~v(r¡w ´j}uy~xw Zxwßw,y~(rHr
(467) yxw&ry{0t tv(r Mr# y < Ãjµáߥ ´Rµµ @gß t wºyxwÝvxw¦ w }*xty¤ty^vxw,y~s*(rty0zs*}uHrtyÝr
(468) Zxw,y¡w#oHµ
(469) ß)}* s*}* tÒr
(470) }* rävxw wvx¨ }\ry&r4³
(471) vxwHry,t0tJ= r ³' *^}uHrºw0r4{ï uy~}uHrjC n Aµ < )®§Ãj 9· @4w}*(rÝ¡rºr
(472) ¥tvxr
(473) wÀryxwHrrÝ ty w,y~zr¢,tyzvx|zv~}uty¡wÝw¶ < j 1Z A· @{,t y~}uwv(r yxwºtèw,y~z¥w,~vxt#ryxyxt_}\rt#r-¡rJ¡r
(474) ~v~}*êºs\r
(475) zs\r}\r
(476) r 0t_j} MHrrj·n R´j}uy~xwÁr
(477) }* r0}*(ry"t~v(ryzs*}uHr ¢ _w,y§yxtvxw&ty§ry~z¥w,xty§r
(478) s* 4v~}u,ty"w,t} r
(479) x|v~}uty r 6w,tv~}\r0ty"v(r[tyHßt wyxw"}* s*}R r 6w,tv~}\C r ¬y~z¥w,~v(r
(480) sty§v(r[tyHß t0wHrr
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(482) vxw _}\rr^tyKvxw,y~(r
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(487) z'*~suty§yxw}* Zxw,yHn"þyvxw,y~s*(rty"r
(488) zvxw,yxw Z(rty§vxw wvxw yxwr0zvxtzv~}uw,rw,y ty:v(r[tyvxws\r}ut rry¬,t2ty: r
(489) sutvxw,yRwF w,xtvxw,yRzvx|zv~}utyAr{¡r
(490) ~v~}*êKw°r
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(492) xwv~}\r
(493) sRr
(494) zvxw,yxw Z(rC t 4§ryxwHrrjßw,yxyxw }\r
(495) s*0w Zxwßwº < ÃjµJá @gn t§°r
(496) z'*~sut"mr
(497) zvxw,yxw Z(r
(498) yxw{r
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(501) N; O,Q GH
(502) 879RMS T8 . t 0wHrr
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(504) v~}*~v(³
(505) v~}utyA2vxw,y~s*(rt"w< 6L1t µjoR@ Zw4vxws\r}ut raräw ´j}uy~x¨ }\räwº,t ' Zxty íî£ïuðEñl vxws\r
(506) vxw,y¤ Z v(r[tävxws\r
(507) v¤,t ty^ r
(508) sutvxw,y zvx|zv~}uty0rèy~rJ¡r
(509) ~v~}*êºwºr
(510) xr,¨ }\rjn Rr
(511) v(rèv(r[tä,t t}uy^,t ' Zxty íî£ïuðEñl vxws\r
(512) vxw,y w,y~(r
(513) ¥wsuw,,w yxw"}*r
(514) surw,yZw"vxws\r}ut r
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(516) vxj}* r
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