The February 1996 Word Ways introduced the concept of a queen\u27s-move-graphable word: place the different letters of a word on a chessboard (extended beyond 8x8, if needed) so as to allow a chess queen to move horizontally, vertically or diagonally to spell out the word in the question

Eckler, A. Ross

English

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202 QUEEN'S-MOVE GRAPHING REVISITED A. ROSS ECKLER Morristown, New Jersey The February 1996 Word Ways introduced the concept of a queen's­move-graphable word: place the different letters of a word on a chessboard (extended beyond 8x8, if needed) so as to allow a chess queen to move horizontally, vertically or diagonally to spell out the word in question. Words that cannot be queen-graphed--and there are only a handful, even in the second or third editions of the unabridged Merriam-Webster--have graphs that can be reduced by elimination of superfluous nodes (letters) and links (queen's-moves between letters) to one or another of a small set of minimal non-queen graphs. A minimal non-queen graph is one which, if any single further link or node (with associated links) is removed, then becomes queen-graphable. Most non-queen-graphable words have graphs that reduce to one of two minimal non-queen graphs, diagrammed below. In the first, all letter-pairs but one (AE) are linked; in the second, a sixth letter joins two letters that are non-adjacent. (The integers characterize the number of links joining each letter; in the second, for example, A,C and E have four links apiece.) A A + + F BCD with BD joined BCD + with FE joined E (44433) E (444332) Words reducible to the first graph include 1DSC1enCes INSEC, intensities INTES, intratnn1tarian INTRA, consciencewise ISCEN, stulti1oquious UTOIL, untrinitarian INTRA, consubstantiationist INSTA, duodenoentero­stomies OENTS, unsubduedness DE S UN; words reducible to the second graph include (2-linked letter in lower case) spectrohelioscopic ePIOSC, pseudoprosperous uORPSE, antispectroscopic ePIOSC, antiecclesiastical lAISEC, protransubstantiation nORTIA, duodenopancreatectomy oNACET, intraorganization rOINTA, tracheochromaticerythroblast aRHOEC, pleuro­lophocerous lUERCO, gastroenterostomies nESORT, transubstantiationalist oNSTAI. There are a handful of Websterian words that reduce to more complex minimal non-queen graphs. Unconscientiousness and unprosperousness both reduce to the identical graphs below (all queen's moves but CO (or EO) are present) S + + + E N + + + P U N C + with NE joined U S 'E + with S P joined o + I (5433333) o + R (5433333) The words tac haematos pectrop which are belie1 C N V TAli I R (VR, CN n R T + E + I + + + S + N + ( U (TS, EC n Leonard Gordon in the form of l the words in t find another mi Or a word grc graphs? It is obvious letters adjacent disease, suprad ecystostomy an Websterian wore The author i~ of likely words different bigrall program for te more stringent It of a queen's­a word on a o allow a chess .0 spell out the .--and there are the unabridged y elimination of tween letters) to ~aphs. A minimal lk or node (with lble. educe to one of n the first, all ;ixth letter joins !rize the n umber A,C and E have ed NSEC, intensities r, stultiloquious duodenoentero­e to the second lioscopic ePIOSC, antiecclesiastical :ectomy oNACET, aRHOEC, pleuro­u bstantiationalist to more complex mprosperousness loves but CO (or 203 The words tactinvariant, sacramentarianism, counterinsurgencies and haematospectrophotometer reduce to the following non-queen graphs which are believed to be minimal. C N V T N S M T A with NI joined I A with TA joined I R (6444222) R C (74333222) (VR, CN not linked) (MC, SN not linked) R R + 0 H T + E + I + + P + + + + with UR joined T + E + M with HA joined S + N + C (65433322) (55433332) U A (TS, EC not linked) (MA not linked) Leonard Gordon notes that tactin variant can be attractively S-graphed in the form of a 3-lobed pinwheel or windmill. It is curious how many of the words in this article have religious connotations. Can any reader find another minimal non-queen graph to which a word graph redllces? Or a word graph which reduces to two different minimal non-queen graphs? It is obvious that any word that has a letter with nine or more other letters adjacent to it is not queen-graphable. Besides the 45-letter lung disease, supradiaphragmatically, epididymodeferentectomies, duodenochol­ecystostomy and choledochoenterstomy appear to be the only such Websterian words. The author is much indebted to Leonard Gordon for providing a list of likely words to test for non-queen-graphability (at least five more different bigrams than different letters). and to Dan Tilque for writing a program for testing any word for queen-graphability (as well as the more stringent king-graphability). h SP joined 33333) 

Queen\u27s-Move Graphing Revisited

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Queen\u27s-Move Graphing Revisited

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