Sum graphs over all the integers
نویسندگان
چکیده
منابع مشابه
Avoiding Zero-sum Subsequences of Prescribed Length over the Integers
Let t and k be a positive integers, and let Ik = {i ∈ Z : −k ≤ i ≤ k}. Let st(Ik) be the smallest positive integer ` such that every zero-sum sequence S over Ik of length |S| ≥ ` contains a zero-sum subsequence of length t. If no such ` exists, then let st(Ik) =∞. In this paper, we prove that st(Ik) is finite if and only if every integer in [1, D(Ik)] divides t, where D(Ik) = max{2, 2k − 1} is ...
متن کاملA Gcd-Sum Function Over Regular Integers Modulo n
We introduce a gcd-sum function involving regular integers (mod n) and prove results giving its minimal order, maximal order and average order.
متن کاملTomorrow and All our Yesterdays: MTL Satisfiability over the Integers
We investigate the satisfiability problem for metric temporal logic (MTL) with both past and future operators over linear discrete bi-infinite time models isomorphic to the integer numbers, where time is unbounded both in the future and in the past. We provide a technique to reduce satisfiability over the integers to satisfiability over the wellknown mono-infinite time model of natural numbers,...
متن کاملOn the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs
For a coloring $c$ of a graph $G$, the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively $sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$, where the summations are taken over all edges $abin E(G)$. The edge-difference chromatic sum, denoted by $sum D(G)$, and the edge-sum chromatic sum, denoted by $sum S(G)$, a...
متن کاملSum-free Sets of Integers
A set S of integers is said to be sum-free if a, b e 5 implies a + b 6 S. In this paper, we investigate two new problems on sum-free sets: (1) Let f(k) denote the largest positive integer for which there exists a partition of (1, 2,... ,f(k)) into k sum-free sets, and let h(k) denote the largest positive integer for which there exists a partition of {1, 2, . . . , h(k)) into k sets which are su...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)00054-u