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Extremal values on the eccentric distance sum of trees
Eccentric distance sum Domination number Leaves Bipartition
2012/7/11
Let $G=(V_G, E_G)$ be a simple connected graph. The eccentric distance sum of $G$ is defined as $\xi^{d}(G) = \sum_{v\in V_G}\varepsilon_{G}(v)D_{G}(v)$, where $\varepsilon_G(v)$ is the eccentricity o...
Note on group distance magic graphs $G[C_4]$
distance magic labeling magic constant sigma labeling graph labeling Abelian group
2012/4/23
A \emph{group distance magic labeling} or a $\gr$-distance magic labeling of a graph $G(V,E)$ with $|V | = n$ is an injection $f$ from $V$ to an Abelian group $\gr$ of order $n$ such that the weight $...
Distance sets of universal and Urysohn metric spaces
Distance sets of universal Urysohn metric spaces Combinatorics
2011/9/20
Abstract: A metric space $\mathrm{M}=(M;\de)$ is {\em homogeneous} if for every isometry $f$ of a finite subspace of $\mathrm{M}$ to a subspace of $\mathrm{M}$ there exists an isometry of $\mathrm{M}$...
Reverse degree distance of unicyclic graphs
Degree Distance Reverse degree distance Diameter Unicyclic graph Pendant vertices Maximum degree
2011/9/1
Abstract: The reverse degree distance is a connected graph invariant closely related to the degree distance proposed in mathematical chemistry. We determine the unicyclic graphs of given girth, number...
Abstract: We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B_3(q) induced on the vertices far from a fixed point, and the subgraph of the dual ...
Abstract: A result of Ben-Or, Coppersmith, Luby and Rubinfeld on testing whether a map be two groups is close to a homomorphism implies a tight lower bound on the distance between the multiplication t...