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the 2-dimension of a tree
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نویسنده
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hedetniemi jason ,hedetniemi stephen ,laskar renu c. ,mulder henry martyn
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منبع
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communications in combinatorics and optimization - 2020 - دوره : 5 - شماره : 1 - صفحه:69 -81
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چکیده
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Let x and y be two distinct vertices in a connected graph g. the x,y-location of a vertex w is the ordered pair of distances from w to x and y, that is, the ordered pair (d(x,w),d(y,w)). a set of vertices w in g is x,y-located if any two vertices in w have distinct x,y-locations. a set w of vertices in g is 2-located if it is x,y-located, for some distinct vertices x and y. the 2-dimension of g is the order of a largest set that is 2-located in g. note that this notion is related to the metric dimension of a graph, but not identical to it. we study in depth the trees t that have a 2-locating set, that is, have 2-dimension equal to the order of t. using these results, we have a nice characterization of the 2-dimension of arbitrary trees.
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کلیدواژه
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resolvability ,location number ,2-dimension ,tree ,2-locating set
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آدرس
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wingate universitywingate universitywingate ncusa, department of mathematics, united states, clemson university, school of computing, united states, clemson university, united states, erasmus universiteit, econometrisch instituut, netherlands
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پست الکترونیکی
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hmmulder@ese.eur.nl
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Authors
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