Displaying similar documents to “Containers and wide diameters of P 3 ( G ) ”

Homogeneously embedding stratified graphs in stratified graphs

Gary Chartrand, Donald W. Vanderjagt, Ping Zhang (2005)

Mathematica Bohemica

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A 2-stratified graph G is a graph whose vertex set has been partitioned into two subsets, called the strata or color classes of G . Two 2 -stratified graphs G and H are isomorphic if there exists a color-preserving isomorphism φ from G to H . A 2 -stratified graph G is said to be homogeneously embedded in a 2 -stratified graph H if for every vertex x of G and every vertex y of H , where x and y are colored the same, there exists an induced 2 -stratified subgraph H ' of H containing y and a color-preserving...

The independent resolving number of a graph

Gary Chartrand, Varaporn Saenpholphat, Ping Zhang (2003)

Mathematica Bohemica

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For an ordered set W = { w 1 , w 2 , ⋯ , w k } of vertices in a connected graph G and a vertex v of G , the code of v with respect to W is the k -vector c W ( v ) = ( d ( v , w 1 ) , d ( v , w 2 ) , ⋯ , d ( v , w k ) ) . The set W is an independent resolving set for G if (1) W is independent in G and (2) distinct vertices have distinct codes with respect to W . The cardinality of a minimum independent resolving set in G is the independent resolving number i r ( G ) . We study the existence of independent resolving sets in graphs, characterize all nontrivial connected graphs G of order...