Let G be a subdivision of a ladder graph. In this paper we study magic evaluation with type (1, 1, 1) for a given any general ladder graph G. We prove that subdivided ladder admits magic evaluation having type (1, 1, 1). We also prove such a subdivision admits consecutive magic evaluation having type (1, 1, 0). AMS (MOS) Subject Classification Codes: 05C78

Isometric subgraphs of hypercubes are known as partial cubes. The subdivision graph of a graph G is obtained from G by subdividing every edge of G. It is proved that for a connected graph G its subdivision graph is a partial cube if and only if every block of G is either a cycle or a complete graph. Regular partial cubes are also considered. In particular it is shown that among the generalized ...

In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph.

In this paper we discuss cordial labeling in context of barycentric subdivision of shell graph, complete bipartite graph Kn,n and wheel graph. AMS subject classification: 05C78.

The domination subdivision number sdγ(G) of a graph is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number. Arumugam showed that this number is at most three for any tree, and conjectured that the upper bound of three holds for any graph. Although we do not prove this interesting conjecture, we give an upp...

We prove that every graph of minimum degree at least r and girth at least 186 contains a subdivision of Krþ1 and that for r5435 a girth of at least 15 suffices. This implies that the conjecture of Haj ! os that every graph of chromatic number at least r contains a subdivision of Kr (which is false in general) is true for graphs of girth at least 186 (or 15 if r5436). More generally, we show tha...

The permanental polynomial of a graph G is π(G,x) , per(xI −A(G)). From the result that a bipartite graph G admits an orientation Ge such that every cycle is oddly oriented if and only if it contains no even subdivision of K2,3, Yan and Zhang showed that the permanental polynomial of such a bipartite graph G can be expressed as the characteristic polynomial of the skew adjacency matrix A(Ge). I...

The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder graph. In particular, we show that the ladder graph Ln with m-pendant Ln mk1 is odd graceful. We also show that the subdivision of ladder graph Ln with m-pendant S(Ln)  mk1 is odd grace...