The graphs, all of whose spanning trees are isomorphic to each other

Multicolored Isomorphic Spanning Trees in Complete Graphs

In this paper, we first prove that if the edges of K2m are properly colored by 2m− 1 colors in such a way that any two colors induce a 2-factor of which each component is a 4-cycle, then K2m can be decomposed into m isomorphic multicolored spanning trees. Consequently, we show that there exist three disjoint isomorphic multicolored spanning trees in any properly (2m−1)-edge-colored K2m for m ≥ 14.

Counting the number of spanning trees of graphs

A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.

Graphs with all spanning trees nonisomorphic

Graphs whose complement and square are isomorphic ( extended version )

We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-complementary graphs, and characterize square-complementary graphs within various graph classes. The bipa...

NUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS

In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...