On the Graceful Game

A graceful labeling of a graph $G$ with $m$ edges consists of labeling the vertices of $G$ with distinct integers from $0$ to $m$ such that, when each edge is assigned as induced label the absolute difference of the labels of its endpoints, all induced edge labels are distinct. Rosa established two well known conjectures: all trees are graceful (1966) and all triangular cacti are graceful (1988). In order to contribute to both conjectures we study graceful labelings in the context of graph games. The Graceful game was introduced by Tuza in 2017 as a two-players game on a connected graph in which the players Alice and Bob take turns labeling the vertices with distinct integers from 0 to $m$. Alice's goal is to gracefully label the graph as Bob's goal is to prevent it from happening. In this work, we study winning strategies for Alice and Bob in complete graphs, paths, cycles, complete bipartite graphs, caterpillars, prisms, wheels, helms, webs, gear graphs, hypercubes and some powers of paths

Graph labeling games

We propose the study of many new variants of two-person graph labeling games. Hardly anything has been done in this wide open field so far. © 2017 Elsevier B.V

Ariel - Volume 11 Number 2

Executive Editors Ellen Feldman Leonardo S. Nasca, Jr. Business .Managers Barbara L. Davies Martin B. Getzow News Editor Aaron D. Bleznak Features Editor Hugh A. Gelabert CAHS Editor Joan M. Greco Editorial Page Editor Samuel Markind Photography Editor Leonardo S. Nasca, Jr. Sports Editor Paul F. Mansfiel

Concordance to the Poems of Henry Howard, Earl of Surrey

Submitted to the Department of English and the Faculty of the Graduate School of the University of Kansas in partial fulfillment of the requirements for the degree of Master of Arts

"a Sceane of Uttmost Vanity": the Spectacle of Gambling in Late Stuart Culture.

Restoration diarist John Evelyn describes a memorable occasion at court on Twelfth Night, 6 January 1662: This evening (according to costóme) his Majestie opned the Réveils of that night, by throwing the Dice himselfe, in the Privy Chamber, where was a table set on purpose, & lost his 100 pounds: the yeare before he won 150 pounds: The Ladys also plaied very deepe: I came away when the Duke of Ormond had won about 1000 pounds & left them still at passage, Cards &c: at other Tables, both there and at the Groome-porters, observing the wiccked folly vanity & monstrous excesse of Passion amongst some loosers, & sorry I am that such a wretched Custome as play to that excesse should be countenanc'd in a Court, which ought to be an example of Virtue to the rest of the kingdome.

The Johnsonian April 26, 1924

The Johnsonian is the weekly student newspaper of Winthrop University. It is published during fall and spring semesters with the exception of university holidays and exam periods. We have proudly served the Winthrop and Rock Hill community since 1923.https://digitalcommons.winthrop.edu/thejohnsonian/1018/thumbnail.jp

Mustang Daily, October 8, 1981

Student newspaper of California Polytechnic State University, San Luis Obispo, CA.https://digitalcommons.calpoly.edu/studentnewspaper/3950/thumbnail.jp