The k-wheel Wk is the graph obtained as a join of a vertex and the cycle of length k. It is proved that a subdivided wheel G embeds isometrically into a hypercube if and only if G is the subdivision graph S(K4) of K4 or G is obtained from the wheel Wk (k¿ 3) by subdividing any of its outer-edges with an odd number of vertices. c © 2003 Elsevier B.V. All rights reserved.

A 4-wheel is a simple graph on 5 vertices with 8 edges, consisting of a 4-cycle, with a fifth vertex joined to each vertex in the 4-cycle. A A-fold 4-wheel system of order n is an edge-disjoint decomposition of AKn into 4-wheels. If two non-adjacent edges of the 4-cycle are removed, the result is a bowtie (that is, two triangles with a common vertex). In this paper necessary and sufficient cond...

Chemical compounds and drugs are often modeled as graphs where each vertex represents an atom of molecule, and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph, and can be different structures. In this paper, we determine the logarithm multiplicative Wiener index and recipr...

Chemical compounds and drugs are often modelled as graphs where each vertex represents an atom of molecule, and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph, and can be different structures. In this paper, by virtue of mathematical derivation, we determine the fourth, f...

In this paper we introduce remainder cordial labeling of graphs. Let $G$ be a $(p,q)$ graph. Let $f:V(G)rightarrow {1,2,...,p}$ be a $1-1$ map. For each edge $uv$ assign the label $r$ where $r$ is the remainder when $f(u)$ is divided by $f(v)$ or $f(v)$ is divided by $f(u)$ according as $f(u)geq f(v)$ or $f(v)geq f(u)$. The function$f$ is called a remainder cordial labeling of $G$ if $left| e_{...

A wheel is a graph made of a cycle of length at least 4 together with a vertex that has at least three neighbors in the cycle. We prove that the problem whose instance is a graph G and whose question is “does G contains a wheel as an induced subgraph” is NP-complete. We also settle the complexity of several similar problems.

A wheel is an induced cycle C plus a vertex connected to at least three vertices of C. Trotignon [14] asked if the class of wheel-free graphs is χ-bounded, i.e. if the chromatic number of every graph with no induced copy of a wheel is bounded by a function of its maximal clique. In this paper, we prove a weaker statement: for every `, the class of graphs with no induced wheel and no induced K`,...