Quadratic embedding constants of hairy cycle graphs

A cycle embedding problem for Cube-Connected Cycles Graphs

Let n be an odd integer with n ≥ 3. The cube-connected cycles graph CCCn has n × 2 vertices, labeled (l,x), where 0 ≤ l ≤ n − 1 and x is an n-bit binary string. Two vertices (l,x) and (l′,y) are adjacent if and only if either x = y and |l − l′| = 1, or l = l′ and y = (x). In this paper, we will find the set of all possible lengths of cycles in CCCn with n is odd and n ≥ 3 .

Fault-tolerant cycle-embedding in alternating group graphs

a r t i c l e i n f o a b s t r a c t In a recently published paper [Z.-J. Xue, S.-Y. Liu, An optimal result on fault-tolerant cycle-embedding in alternating group graphs, Inform. the authors showed that for a set of faulty vertices F in an n-dimensional alternating group graph AG n , AG n − F remains pancyclic if |F | 2n − 6. However, the proof of the result is flawed. We will prove the theore...

Quadratic Surface Embedding

We discuss various primal and dual algorithms for multidimensional scaling with spherical, ellipsoidal, and more general quadratic constraints. Distances between points on the surface can be either measured along Euclidean lines or along shortest geodesics on the surface.

α Valuations of Special Classes of Quadratic Graphs

INTEGER-MAGIC SPECTRA OF CYCLE RELATED GRAPHS

For any h in N , a graph G = (V, E) is said to be h-magic if there exists a labeling l: E(G) to Z_{h}-{0} such that the induced vertex set labeling l^{+: V(G) to Z_{h}} defined by l^{+}(v)= Summation of l(uv)such that e=uvin in E(G) is a constant map. For a given graph G, the set of all for which G is h-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper, the ...