Bandwidth labelling is a well known research area in graph theory. We provide a new proof that the bandwidth of Mobius ladder is 4, if it is not a $K_{4}$, and investigate the bandwidth of a wider class of Mobius graphs of even strips.

In social networks, a role assignment is such that individuals play the same role, if they relate in way to other playing counterpart roles. As simple graph models network rises decision problem called r -Role Assignment whether it exists an of distinct roles vertices graph. This known be NP-complete for any fixed ? 2. The Cartesian product graphs one most studied operation on and has numerous ...

Given a Cartesian product G = GI x x G,, (m > 2) of nontrivial connected graphs G, and the base d, dimension D de Bruijn graph B(d,D), it is investigated under which conditions G is (or is not) a subgraph of B(d, D). We present a complete solution of this problem for the case D 3 4. For D = 3, we give partial results including a complete solution for the case that G is a torus, i.e., G is the C...

When is the Cartesian product of two graphs the graph of a polytope, of a cellular sphere, or even of a combinatorial manifold? In this note, we determine all 3-polytopal complexes whose graph is the Cartesian product of a 3-cycle by a Petersen graph. Through this specific example, we showcase certain techniques which seem relevant to enumerate all polytopal complexes realizing a given product....

Suppose ρ is a simple graph, then its eccentric harmonic index defined as the sum of terms id="M2"> 2 / e a + b for edges id="M3"> v , where id="M4"> eccentricity id="M5"> th vertex graph id="M6"> . ...

In11, Kulli and Janakiram initiate the concept of maximal domination in graphs. In this paper, we obtained some bounds characterizations. Also, estimate value number graph products such as join graphs, corona product, cartesian product strong product.

It is well-known that all finite connected graphs have a unique prime factor decomposition (PFD) with respect to the strong graph product which can be computed in polynomial time. Essential for the PFD computation is the construction of the so-called Cartesian skeleton of the graphs under investigation. In this contribution, we show that every connected thin hypergraph H has a unique prime fact...