ary TRANSIT FUNCTIONS IN GRAPHS
نویسندگان
چکیده
n-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural n-ary generalization of geodesicaly convexity. Furthermore, we generalize the betweenness axioms to n-ary transit functions and discuss the connectivity conditions for underlying hypergraph. Also n-ary all paths transit function is considered.
منابع مشابه
N-ary Transit Functions in Graphs
n-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural n-ary generalization of geodesicaly convexity. Furthermore, we generalize the betweenness axioms to n-ary transit functions and discuss the connectivity conditions for underlying hypergr...
متن کاملStrongly regular graphs constructed from p-ary bent functions
In this paper, we generalize the construction of strongly regular graphs in Tan et al. (J. Comb. Theory, Ser. A 117:668–682, 2010) from ternary bent functions to p-ary bent functions, where p is an odd prime. We obtain strongly regular graphs with three types of parameters. Using certain non-quadratic p-ary bent functions, our constructions can give rise to new strongly regular graphs for small...
متن کاملTriangle path transit functions, betweenness and pseudo-modular graphs
The geodesic and induced path transit functions are the two well-studied interval functions in graphs. Two important transit functions related to the geodesic and induced path functions are the triangle path transit functions which consist of all vertices on all u, v-shortest (induced) paths or all vertices adjacent to two adjacent vertices on all u, v-shortest (induced) paths, for any two vert...
متن کاملPARTIAL DIFFERENCE SETS FROM p-ARY WEAKLY REGULAR BENT FUNCTIONS AND QUADRATIC FORMS
We generalize the construction of affine polar graphs in two different ways to obtain partial difference sets and amorphic association schemes. In the first generalization we replace the quadratic form in the affine polar graph construction by higher degree homogeneous functions that are p-ary weakly regular bent. The second generalization uses a combination of quadratic forms and uniform cyclo...
متن کاملIndependence Results for n-Ary Recursion Theorems
The n-ary first and second recursion theorems formalize two distinct, yet similar, notions of self-reference. Roughly, the n-ary first recursion theorem says that, for any n algorithmic tasks (of an appropriate type), there exist n partial computable functions that use their own graphs in the manner prescribed by those tasks; the n-ary second recursion theorem says that, for any n algorithmic t...
متن کامل