Titlebook: ;

Gobble

https://doi.org/10.1007/978-3-662-67273-0 well-known “scissors, paper and stone” game, is considered. We show that in a tournament game, both the players have a unique optimal strategy. We then consider incidence matrix games, where the payoff matrix is the incidence matrix of a directed graph. A graph-theoretic description of the value and the optimal strategies is provided.

喷出

北极熊

Cycles and Cuts,djacency matrix of a regular graph and that of its complement and line graph. Several results in this direction are proved in the next section. In the final section we derive spectral properties of strongly regular graph and apply them to derive the well-known Friendship Theorem.

单挑

Medley

optional

https://doi.org/10.1007/978-1-4613-2643-4that bring out the connection between the distance matrix and the Laplacian of a tree. A formula for the inverse of the distance matrix, due to Graham and Lovaász, is proved. In the final section we prove some properties of the eigenvalues of the distance matrix of a tree.

可憎

华而不实

启发

懒洋洋

Adjacency Matrix,ted. The Matrix-Tree Theorem and some related results are proved. Bounds for the Laplacian spectral radius are obtained. The edge-Laplacian is considered and a formula for the inverse of the edge-Laplacian of a tree is obtained. In the process we also obtain a formula for the Moore-Penrose inverse o