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Association: Name: The Mathematical Association of America MathFest URL: http://www.maa.org
Citation: URL: http://www.allacademic.com/meta/p275715_index.html Direct Link: HTML Code:

Gera, Ralucca., Eroh, Linda., Winters, Steven. and Bullington, Grady. "Pizza Delivery: 2-Stop-Return Distances in Graphs" Paper presented at the annual meeting of the The Mathematical Association of America MathFest, TBA, Madison, Wisconsin, Jul 28, 2008 <Not Available>. 2008-09-03 <http://www.allacademic.com/meta/p275715_index.html>

Gera, R. , Eroh, L. , Winters, S. J. and Bullington, G. (2008, Jul) "Pizza Delivery: 2-Stop-Return Distances in Graphs" Paper presented at the annual meeting of the The Mathematical Association of America MathFest, TBA, Madison, Wisconsin <Not Available>. 2008-09-03 from http://www.allacademic.com/meta/p275715_index.html

Publication Type: Conference Paper/Unpublished Manuscript Abstract: Recall that the distance of a vertex $x$ is $ d(x) = \sum_{\forall u \in V(G)} d(x,u).$ We define the {\it $2$-stop-return} distance of $x$ with two stops at $y$ and $z$ ($y \neq z$) to be $$d_{2s} (x,\{y,z\}) = d(x,y) + d(y,z) + d(z,x).$$ %For simplicity, we will write $d_{2s}(x,y,z)$ instead of $d_{2s}(x,\{y,z\})$. \vspace{.5cm} \noindent The {\it $2$-stop-return eccentricity $e_{2s}(x)$} of a vertex $x$ in a graph $G$ is the maximum $2$-stop-return distance from $x$, that is, $$e_{2s} (x) = \max_{y, z \in V(G)} \bigg(d(x,y) + d(y,z) + d(z,x)\bigg).$$ The minimum $2$-stop-return eccentricity among the vertices of $G$ is the {\it $2$-stop-return radius} that is, $\rm rad_{2s} (G) = \min_{x \in V(G)}e_{2s} (x)$. The maximum $2$-stop-return eccentricity among the vertices of $G$ is the {\it $2$-stop-return diameter} that is, $\rm diam_{2s} (G)$ $=$ $\max_{x \in V(G)} e_{2s} (x).$ \vspace{.3cm} \noindent This particular metric minimizes the distance that a pizza delivery guy would need to travel if he wants to make two deliveries in one trip. We present results about the $2$-stop-return distance in graphs.

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Distance Properties of Graphs

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