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Strong edge geodetic problem in networks

100%

Manuel P., Klavžar S., Xavier A., Arokiaraj A., Thomas E.

Open Mathematics

2017

tom 15

nr 1

1225-1235

Geodesic covering problems form a widely researched topic in graph theory. One such problem is geodetic problem introduced by Harary et al. [Math. Comput. Modelling, 1993, 17, 89-95]. Here we introduce a variation of the geodetic problem and call it strong edge geodetic problem. We illustrate how this problem is evolved from social transport networks. It is shown that the strong edge geodetic problem is NP-complete. We derive lower and upper bounds for the strong edge geodetic number and demonstrate that these bounds are sharp. We produce exact solutions for trees, block graphs, silicate networks and glued binary trees without randomization.

A class of extensions of Restricted (s,t)-Wythoff’s game

88%

Liu S., Li H.

Open Mathematics

2017

tom 15

nr 1

281-295

Restricted (s, t)-Wythoff’s game, introduced by Liu et al. in 2014, is an impartial combinatorial game. We define and solve a class of games obtained from Restricted (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The results show that under certain conditions they are equivalent to one case in which only one P-position is adjoined as an additional move. Furthermore, two winning strategies of exponential and polynomial are provided for the games.

Ograniczanie wyników

2 Open Mathematics

1 Arokiaraj A.

1 Klavžar S.

1 Li H.

1 Liu S.

1 Manuel P.

1 Thomas E.

1 Xavier A.

2 2017

Wyniki wyszukiwania

Strong edge geodetic problem in networks

A class of extensions of Restricted (s,t)-Wythoff’s game