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Non-Isolated Resolving Sets of Corona Graphs with Some Regular Graphs
Let G be a connected, simple, and finite graph. For an ordered set W={w1,w2,…,wk}⊆V(G) and a vertex v of G, the representation of v with respect to W is the k-vector r(v|W)=(dG(v,w1),…,dG(v,wk)).
Wahyuni Abidin+2 more
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Let and be simple graphs. We write to mean that any red–blue coloring of all edges of will contain either a red copy of or a blue copy of A graph (without isolated vertices) satisfying and for each is called a Ramsey -minimal graph. The set of all Ramsey
Kristiana Wijaya+3 more
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Restricted size Ramsey number for path of order three versus graph of order five
Let $G$ and $H$ be simple graphs. The Ramsey number for a pair of graph $G$ and $H$ is the smallest number $r$ such that any red-blue coloring of edges of $K_r$ contains a red subgraph $G$ or a blue subgraph $H$.
Denny Riama Silaban+2 more
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On The Partition Dimension of Disconnected Graphs
For a graph G=(V,E), a partition Ω=\{O_1,O_2,…,O_k \} of the vertex set V is called a resolving partition if every pair of vertices u,v∈V(G) have distinct representations under Ω.
Debi Oktia Haryeni+2 more
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On the Restricted Size Ramsey Number Involving a Path P3
For any pair of graphs G and H, both the size Ramsey number ̂r(G,H) and the restricted size Ramsey number r*(G,H) are bounded above by the size of the complete graph with order equals to the Ramsey number r(G,H), and bounded below by e(G) + e(H) − 1 ...
Silaban Denny Riama+2 more
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Hadamard matrices of order 36 and double-even self-dual [72,36,12] codes [PDF]
Before this work, at least 762 inequivalent Hadamard matrices of order 36 were known. We found 7238 Hadamard matrices of order 36 and 522 inequivalent [72,36,12] double-even self-dual codes which are obtained from all 2-(35,17,8) designs with an ...
Iliya Bouyukliev+2 more
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The complete list of Ramsey $(2K_2,K_4)$-minimal graphs
Let $F, G,$ and $H$ be non-empty graphs. The notation $F \rightarrow (G,H)$ means that if all edges of $F$ are arbitrarily colored by red or blue, then either the subgraph of $F$ induced by all red edges contains a graph $G$ or the subgraph of $F ...
Kristiana Wijaya+3 more
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On the enumeration of uniquely reducible double designs [PDF]
A double $2$-$(v,k,2 \lambda)$ design is a design which is reducible into two $2$-$(v,k,\lambda)$ designs. It is called uniquely reducible if it has, up to equivalence, only one reduction.
Veerle Fack+2 more
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A combinatorial proof of a partition identity of Andrews and Stanley [PDF]
In his paper, "On a Partition Function of Richard Stanley," George Andrews proves a certain partition identity analytically and asks for a combinatorial proof. This paper provides the requested combinatorial proof.
arxiv +1 more source
Trees with Certain Locating-chromatic Number
The locating-chromatic number of a graph G can be defined as the cardinality of a minimum resolving partition of the vertex set V(G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in G are ...
Dian Kastika Syofyan+2 more
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