Let Hn be the number of claw-free cubic graphs on 2n labeled nodes. In an earlier paper we characterized claw-free cubic graphs and derived a recurrence relation for Hn. Here

We give new examples of graphs with the n-e.c. adjacency property. Few explicit families of n-e.c. graphs are known, despite the fact that almost all …nite graphs are n-e.c. Our examples are collinearity graphs of certain partial planes derived from a¢ ne planes of even order. We use probabilistic and geometric techniques to construct new examples of n-e.c. graphs from partial planes for all n,...

In this paper, we first introduce a novel class of graphs, namely supergrid. Supergrid graphs include grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for grid graphs and triangular grid graphs were known to be NP-complete. However, they are unknown for supergrid graphs. The Hamiltonian cycle (path) problem on supergrid graphs can be applied to ...

We discuss how interleavers for parallel concatenated turbo codes with good minimum distance can be derived from graphs having large girth, i.e. graphs whose length of the shortest cycle is large.

The forgotten topological index of a molecular graph $G$ is defined as $F(G)=sum_{vin V(G)}d^{3}(v)$, where $d(u)$ denotes the degree of vertex $u$ in $G$. The first through the sixth smallest forgotten indices among all trees, the first through the third smallest forgotten indices among all connected graph with cyclomatic number $gamma=1,2$, the first through<br /...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Keywords: Balanced graphs 1-balanced graphs Cartesian product of graphs Web graphs a b s t r a c t There are several density...

The secure domination numbers of the Cartesian products two small graphs with paths or cycles is determined, as well for Möbius ladder graphs. Prior to this work, in all cases where number has been proof either trivial, derived from lower bounds established by considering different forms domination. However, latter mode not applicable most graphs, including those considered here. Hence, work re...

In this paper, we first introduce a novel class of graphs, namely supergrid. Supergrid graphs include grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for grid graphs and triangular grid graphs were known to be NP-complete. However, they are unknown for supergrid graphs. The Hamiltonian cycle (path) problem on supergrid graphs can be applied to ...

the eccentricity connectivity index of a molecular graph g is defined as (g) = av(g)deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to othervertices of g and deg(a) is degree of vertex a. here, we compute this topological index forsome infinite classes of dendrimer 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...