We study the Laplacian spectrum of token graphs, also called symmetric powers graphs. The k -token graph F ( G ) a is whose vertices are -subsets from , two which being adjacent whenever their difference pair in . In this paper, we give relationship between spectra any graphs given graph. particular, show that, for integers h and such that 1 ≤ n 2 contained doubled odd Johnson can be obtained a...

A chain packing H in a graph is a subgraph satisfying given degree constraints at the vertices. Its size is the number of odd degree vertices in the subgraph. An odd subtree packing is a chain packing which is a forest in which all non-isolated vertices have odd degree in the forest. We show that for a given graph and degree constraints, the size of a maximum chain packing and a maximum odd sub...

An odd neighborhood transversal of a graph is a set of its vertices that intersects the set of neighbors of each of its vertices in an odd number of elements. In the case of grid graphs this odd number will be either one or three. We characterize those grid graphs that have odd neighborhood transversals.

A geodominating set S ⊆ V of a graph G is said to be an odd geo-dominating if for every vertex , and The minimum cardinality the called geo-domination number denoted by . with – G. We develop algorithm compute graphs some families graphs.

We deal with Oberwolfach factorizations of the complete graphs Kn and K n *, which admit a regular group of automorphisms. We show that the existence of such a factorization is equivalent to the existence of a certain difference sequence defined on the elements of the automorphism group, or to a certain sequencing of the elements of that group. In the particular case of a hamiltonian factorizat...

A radio coloring of a graph G is an assignment of nonnegative integers to its nodes so that each pair of adjacent nodes have color numbers that differ by at least two, and any pair of nodes at distance 2 have different colors. Every graph has a radio coloring by simply assigning the odd integers 1, 3, 5, ......, but there is then a big difference between the smallest and largest colors. We defi...