The CARTESIAN PRODUCT (CROSS PRODUCT)
Cycle decompositions of the Cartesian product of cycles
... Corollary 1.6 For even r ≥ 4, the hypercube Q r can be decomposed into 4 r-cycles. This solves the Problem 1.1 for the case k = 4r. As the structure of the Cartesian product of cycles is recursive, use of ...
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2 The distinguishing index of the Cartesian product
... Proposition 1.3. Let G be the Cartesian product of two graphs G 1 and G 2 . Then D 0 (G 1 2G 2 ) = 1 if and only if G 1 and G 2 are relatively prime and both are asymmetric graphs. The aim of this paper is ...
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The distinguishing index of the Cartesian product of finite graphs ∗
... the Cartesian product of a star K 1,n of size n and a path P m of order m is greater than 2 whenever n > 2 2m+1 ...the Cartesian product of two graphs with widely different orders and sizes ...
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k-tuple colorings of the Cartesian product of graphs
... The cartesian product GH of two graphs G and H has vertex set V (G) × V (H), two vertices being joined by an edge whenever they have one coordinate equal and the other ...This product is commutative ...
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On the stability of the Cartesian product of a neural ring and an arbitrary neural network
... This paper is structured as follows. In Section , formal definitions of the Cartesian product of neural networks, ring and linear configuration of a network are stated. In Sec- tion , it is proven that by ...
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On the Signed Domination Number of the Cartesian Product of Two Directed Cycles
... Shaheen and Salim in [11], were studied the signed domination number of two directed cycles C m × C n when m = 3, 4, 5, 6, 7 and arbitrary n. In this paper, we study the Cartesian product of two directed ...
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Completeness and compactness of the Cartesian product of two soft metric spaces
... In 2010, in order to introduce soft set relations, Babitha and Sunil gave a definition of the Carte- sian product of two soft sets. In 2013, Das and Samanta introduced the notion of soft metric space by using a ...
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On the Cycle Indices of the Cyclic and Dihedral Groups Acting on the Cartesian Product Of X
... The concept of cycle index of various group actions has been studied by a number of authors since inception of the concept by Howard Redfield. However we observe that the cycle index of cyclic group acting on ...
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On Total Regularity of the Cartesian product of two Interval – valued Fuzzy Graphs
... the Cartesian product of two interval – valued fuzzy graphs (IVFG) and investigate the total regularity of the Cartesian ...the Cartesian product of two totally regular interval – ...
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Orientable Z n -distance magic labeling of the Cartesian product of two cycles
... 4 Future work We have shown that the Cartesian product of any two cycles is orientable Z n -distance magic. In this paper, we fix the orientation of our cycles. However, because any cycle can be oriented in ...
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Orientable Z n -distance magic labeling of the Cartesian product of many cycles
... ` for − → G , we say that G is orientable Z n -distance magic and the directed Z n -distance magic labeling − → ` we call an orientable Z n -distance magic labeling . In this paper, we find orientable Z n - distance ...
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Ecstatic Type Inference for Ruby Using the Cartesian Product Algorithm
... Adding a singleton method to a Ruby object corresponds to creating a new sub- type in a traditional class based language like Java.. The new class will be a subclass of the old, and the [r] ...
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b-Continuity Properties of the Cartesian Product of Tadpole Graphs and Paths
... A proper k-coloring of a graph G is an assignment of k-colors to the vertices of G such that no two adjacent vertices are assigned the same color.. Later, new types of vertex colo[r] ...
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2 Connectivity of Cartesian product
... Cartesian product. Math. Subj. Class.: 05C40, 05C76 1 Introduction The Cartesian product has been studied extensively since the ...a Cartesian product and how it depends on ...
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Restricted Connectivity of Cartesian Product Graphs
... of Cartesian Product Graphs Laihuan Chen, Jixiang Meng, Yingzhi Tian, Fengxia Liu ∗ Abstract—For a connected graph G = (V (G), E(G)), a vertex set S ⊆ V (G) is a k-restricted vertex-cut if G − S is ...
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On the Graceful Cartesian Product of Alpha-Trees
... Let f be an α-labeling of a tree G of size n with boundary value λ. Suppose that f is transformed into a d-graceful labeling shifted c units. Then the stable set A receives the labels c, c + 1, ..., c + λ and the stable ...
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Cartesian product and Neighbourhood Polynomial of a Graph
... Here the neighbourhood polynomial for the graphs planar grids, ladder graphs, torus grids, prisms, which are formed by the Cartesian product of two graphs are calculated. Also tried to give one ...
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The reliability Wiener number of cartesian product graphs
... Definition 1 The Cartesian product of weighted graphs and is a weighted graph, denoted as □ , whose vertex set is ( □ ) = ( ) × ( ). Two vertices = ( , ) and = ( , ) of □ are adjacent if = ∈ ( ) or = ∈ ( ). ...
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STATUS CONNECTIVITY INDICES OF CARTESIAN PRODUCT OF GRAPHS
... such product graphs are related to the corresponding invariants of the original ...graph product is Cartesian ...using Cartesian product of graphs see [17, 20, 21, 22]. The ...
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For updated version of this document see CARTESIAN PRODUCT
... Some arrangements get close to this basic fact. For example, the child can put the 60 cubes into five 3×2×2 stacks, and cubes in each stack are marked with the same number. In the Cartesian product, the ...
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