an acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. the acyclic chromatic index of a graph $g$ denoted by $chi_a '(g)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. the maximum degree in $g$ denoted by $delta(g)$, is the lower bound for $chi_a '(g)$. $p$-cuts introduced in this paper acts as a powerfu...

The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r-edges of G, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number lc(G) of a graph G is the least positive integer r for which Lr(G) ...

The establishment of the Croatian National Spatial Data Infrastructure has started at the beginning of the 1990's. The main agitator of the activities was the State Geodetic Administration of the Republic of Croatia. They started to build the documentation that describe vision and goals, while through studies and pilot projects they developed procedures and exact steps for realization of the go...

In 1998 Land Information New Zealand introduced New Zealand Geodetic Datum 2000 (NZGD2000) as its new national datum. It is defined as a semi-dynamic datum and incorporates a national deformation model to ensure that the accuracy of the datum is maintained. The deformation model allows observations made at an epoch other than the datum reference epoch of 2000.0 to be modeled so that coordinates...

We show that the geodetic game, introduced by Fraenkel and Harary, is decidable in polynomial time on AT-free graphs.

A k-geodetic digraph G is a digraph in which, for every pair of vertices u and v (not necessarily distinct), there is at most one walk of length ≤ k from u to v. If the diameter of G is k, we say that G is strongly geodetic. Let N(d, k) be the smallest possible order for a k-geodetic digraph of minimum out-degree d, then N(d, k) ≥ 1 + d+ d2 + . . .+ dk = M(d, k), where M(d, k) is the Moore boun...

‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $abin E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $sum S(G)$‎, ‎a...

A recent variation of the classical geodetic problem, the strong geodetic problem, is defined as follows. If G is a graph, then sg(G) is the cardinality of a smallest vertex subset S, such that one can assign a fixed geodesic to each pair {x, y} ⊆ S so that these (|S| 2 ) geodesics cover all the vertices of G. In this paper, the strong geodetic problem is studied on Cartesian product graphs. A ...

A decade of observations in geodetic mode with the VLBA network gave valuable results. Approximately 1/5 of all geodetic observations are recorded in VLBA mode and processed at the Socorro correlator. Ten years of observations allowed us to reliably measure slow intra-plate motion of the VLBA stations located on the North-American plate. It also helped us to achieve scientific objectives of geo...