We develop Stone relation algebras, which generalise relation algebras by replacing the underlying Boolean algebra structure with a Stone algebra. We show that finite matrices over bounded linear orders form an instance. As a consequence, relation-algebraic concepts and methods can be used for reasoning about weighted graphs. We also develop a fixpoint calculus and apply it to compare different...

in the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(p,q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}a_{l}xb_{l}+overset{v} ‎{underset{s=1}{sum}}c_{s}widetilde{x}d_{s}=f$‎. ‎by this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎when the‎ ‎matrix equation is consistent over...

We examine the binary codes C2(Ai + I) from matrices Ai + I where Ai is an adjacency matrix of a uniform subset graph Γ(n, 3, i) of 3-subsets of a set of size n with adjacency defined by subsets meeting in i elements of Ω, where 0 ≤ i ≤ 2. Most of the main parameters are obtained; the hulls, the duals, and other subcodes of the C2(Ai + I) are also examined. We obtain partial PD-sets for some of...

In the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} ‎{underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$‎. ‎By this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎When the‎ ‎matrix equation is consistent over...

Let  be a set with  elements. A subset  of  ×  is a binary relation (or relation) on . The number of relations on  is 22. Equivalently, there are 2 2 labeled bipartite graphs on 2 vertices, assuming the bipartition is fixed and equitable. A relation  on  is reflexive if for all  ∈ , we have ( ) ∈ . The number of reflexive relations on  is 2(−1). A relation  on  is antisymm...

It is shown that, for a finitely-complete category C with coequalizers of kernel pairs, if every product-regular epi is also stably-regular then there exist the reflections (R)Grphs(C) → (R)Rel(C), from (reflexive) graphs into (reflexive) relations in C, and Cat(C) → Preord(C), from categories into preorders in C. Furthermore, such a sufficient condition ensures as well that these reflections d...

Let G be a connected, simple, and undirrected graph, where V (G) is the vertex set E(G) edge set. k natural numbers. For graph we define total k−labeling ρ such that vertices of are labeled with {0, 2, 4, . , 2kv} edges {1, 3, ke}, = max{2kv, ke}. Total called an irregular reflexive k− labeling if every two distinct have weights, weight defined as sum label incident to this edge. The minimum ha...

We define a total k-labeling φ of graph G as combination an edge labeling φe:E(G)→{1,2,…,ke} and vertex φv:V(G)→{0,2,…,2kv}, such that φ(x)=φv(x) if x∈V(G) φ(x)=φe(x) x∈E(G), where k= max {ke,2kv}. The is called irregular reflexive every two different edges has distinct weights, the weight defined summation label itself its labels. Thus, smallest value k for which strength G. In this paper, we ...

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