A chess board of size m x n can be translated to a Queen\u27s graph in which vertices are adjacent if their squares on the board are in the same row, column, or diagonal. In this research, the total dominator coloring of a Queen\u27s graph is explored, yielding a conjecture for the general m x n case

Smith, Fiona

English

College of Saint Benedict and Saint John’s University: DigitalCommons@CSB/SJU

College of Saint Benedict and Saint John's University DigitalCommons@CSB/SJU Celebrating Scholarship and Creativity Day (2018-) Undergraduate Research 4-27-2023 Total Dominator Coloring on the Queen's graph Fiona Smith College of Saint Benedict/Saint John's University, fsmith001@csbsju.edu Follow this and additional works at: https://digitalcommons.csbsju.edu/ur_cscday  Part of the Mathematics Commons Recommended Citation Smith, Fiona, "Total Dominator Coloring on the Queen's graph" (2023). Celebrating Scholarship and Creativity Day (2018-). 212. https://digitalcommons.csbsju.edu/ur_cscday/212 This Poster is brought to you for free and open access by DigitalCommons@CSB/SJU. It has been accepted for inclusion in Celebrating Scholarship and Creativity Day (2018-) by an authorized administrator of DigitalCommons@CSB/SJU. For more information, please contact digitalcommons@csbsju.edu. TOlAL (mTuAffi A \?, C -~-t3J 1Lf' L) f "I= 151 ,1, {J. t G -\--\ T j3 f t41 ,si •Q LJ,Y A {IQOO.<)J'lC!2.Y\l -1<:> Gl-\3lNO : ~ -\-111<.\v\0~: 5 I BDGI-ICl?: 5 t,JL 1-'\N~ : tf J AC..1-W ·. l-f ~ 81)(;\v\: 3 L- i\C.fFM\\J: 1. c::=t> DEF\Nrno~ "i''O\''-' (O\o,,~ , eUL\o \J'-1"'\C IS aap~I\\ tu all o\\\n., <010,s JC0UOO.\'\'I ~'<<ll;M· \le•-1--i~ o.,e adjQ<.R.!\t ,~ -\nll.'j Q\t IV\ SO-IWZ lCl\JJ, (Cl\\JmY\, 01 c).1u5\JY\Q\ B C D E C.D\'.-LN?: 3 DLMO ·. 1 /\1N r : d--. A-£J:1M0 : 5 f M ~c.F~~~: 1 .._ ____________ --1 N ,.,,rn-£0t.. : a G -H o Q . I..\ ,':, A. J-. -:r. :3 0 A~\)f\-\I :5 -\()I chi'\. 'pc:,o.,d\; {ol \'l:a,?, ;(_~ (0,,1'\)' 4 °? BCtG:r::r·- 4 '"' 0 ?:'-1 1-.~ (Q.i,nJ' Y\. WPIN • O,,Y A {11)1'\0.dJo.~I\-\ "' f, -1-\ , a r_ 1. · 3 \s nunodjOU.\'\\ -\0 V, · C !\!iY\OcljU~Y\\ \<l \), \-\ : l-/ D Y\t:,,'\OdJO.U.'I\\ -\-u C, T ·. '5 f V\uV\OdjUCJlV\t -t<> "'""'e ', 1-":f \'\()V1odjaCJlV\-t -1:-u (;, G : ~ G !\()V\O.djUCR.\l\l ..., B, f ·. '3 ti V\O\'\O.dj Clt.Q.n \ -1<> /\ ('., : 1-j l Y\u\'\actj CIU.l'I"\ -lo "£,, 1) : S A: i flW-L G :S 1?,l'L B : '5 ('ilJL .\-1 : 3 /\C (' 3 t>H1\:. lJ \,; : "J : ' l!,l:Y:l D : LJ n"'" T : a iacn-B' 3 C :Lf j :lf ¥-- :S Q: 4 'R :5 S, 1 1 : d {Q, 3 • V\. 't>oo.,ds: -\'o, I'\= 3, 4 fa n z 5 '"Yd (0,.nl = 5 _l/' "X_~ (Q"3 ,n): Y\. E: : a 1 L ',(_·.i_P..COI' f : 1.. 1\0¥- l : s P.SH, D: 5 L- : i l: : 5 Y1: 1 ~ : 1 N 'J. G ·J. Q: 3 -%-H :3 -p: 4 = I l fo, 1Mn 'oao.1d~ : tO'f rn ~ m<l 'i. ;t( 01n,o)' IY\•d-/ i..-- l fo, m 2'. m1.} l_d(Om.n)= r\. . '-J,/ 0 €.\112.1 "'JQ.,~)(. •' o'< "~cttcwe" on -\-tie. boo..\d h.Cl.S. 0- \'\Q.-1-\JJG\',<. ~ CJ::Jr(\'('(10/1\ Y\CiX\-0..dflle.\'IC.le.S l..."-\-o..\ nu.m'oex ot; \J~\-r,<.QS ct,w1ecl \:>u • \-'r.<2. ,u J f\r\e. ~1~ o~ J..\i\e ~t-rwGt¥-- 0,t\d.) I'\. c.Cl\l\,s \'\,Q.~de.d. O.-t o.. l'Y\iY\\\'Y\V..V\r\ .Q 3 1o. A :S . ½ ,a (: 4 l) :3 t :1 v--: 5 G=J.. \--1 I.'· 3 "}:1. '(.. :4 L d-\-'\ w 3 o, 1 i) : 4 Q: ':i I< 

Total Dominator Coloring on the Queen\u27s graph

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Total Dominator Coloring on the Queen\u27s graph

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