Refereed Journal Articles

  • [54] J. Jerebic, S. Klavzar and D.F. Rall, Distance-balanced graphs, Annals of Combinatorics,
    12 (2008) 71-79.

  • [53] B. Bresar, M.A. Henning and D.F. Rall, Rainbow domination in graphs, Taiwanese Journal of Mathematics,
    12 (2008) 213-225.

  • [52] P. Dorbec, M. Henning and D.F. Rall, On the upper total domination number of Cartesian products of graphs,
    Journal of Combinatorial Optimization, 16 (2008) 68-80.

  • [51] S.M. Hedetniemi, S.T. Hedetniemi, J. Knisely and D.F. Rall, Secondary domination in graphs, AKCE International
    Journal of Graphs and Combinatorics
    , 5 No. 2 (2008) 103-115.

  • [50] W. Goddard, J. Harris, S.M. Hedetniemi, S.T. Hedetniemi, and D.F. Rall, Broadcast chromatic numbers of graphs,
    Ars Combinatoria, 86 (2008) 33-49.

  • [49] B. Bresar, S. Klavzar and D.F. Rall, On the packing chromatic number of Cartesian products, hexagonal lattice, and
    trees, Discrete Applied Mathematics, 155 (2007) 2303-2311.

  • [48] W. Imrich, S. Klavzar and D.F. Rall, Cancellation properties of products of graphs, Discrete Applied Mathematics,
    155 (2007) 2362-2364.

  • [47] B. Bresar, M.A. Henning and D.F. Rall, Paired-domination of Cartesian products of graphs, Utilitas Mathematica,
    73 (2007) 255-265.

  • [46] B. Bresar, S. Klavzar and D.F. Rall, Dominating direct products of graphs, Discrete Mathematics, 307(13) (2007) 1636-1642.

  • [45] B. Bresar, Art Finbow, S. Klavzar and D.F. Rall, On the Packing Chromatic Number of Trees, Cartesian Products and
    Some Infinite Graphs. Electronic Notes in Discrete Mathematics, Vol 30C (2008) 57-61.

  • [44] R. Gallant, G. Gunther, B. Hartnell and D.F. Rall, Limited packings in graphs. Electronic Notes in Discrete Mathematics,
    Vol 30 (2008) 15-20.

  • [43] R.C. Brigham, T.W. Haynes, M.A. Henning and D.F. Rall, Bicritical domination, Discrete Mathematics 305(1-3) (2005) 18-32.

  • [42] W. Imrich and D.F. Rall, Finite and infinite hypercubes as direct products, The Australasian Journal of Combinatorics
    36 (2006) 83-90.

  • [41] R.P. Gallant, G. Gunther, B.L. Hartnell and D.F. Rall, A game of edge removal on graphs, Journal of Combinatorial
    Mathematics and Combinatorial Computing
    57 (2006) 75-82.

  • [40] M.A. Henning and D.F. Rall, On the total domination number of Cartesian products of graphs, Graphs and Combinatorics
    21 (2005) 63-69.

  • [39] B.L. Hartnell and D.F. Rall, On graphs having uniform size star factors, The Australasian Journal of Combinatorics
    34 (2006) 305-311.

  • [38] D.F. Rall, Total domination in categorical products of graphs, Discussiones Mathematicae Graph Theory 25(1-2) (2005) 35-44.

  • [37] B.L. Hartnell and D.F. Rall, On dominating the Cartesian product of a graph and K_2, Discussiones Mathematicae
    Graph Theory
    24(3) (2004) 389-402.

  • [36] B.L. Hartnell and D.F. Rall, Improving some bounds for dominating Cartesian products, Discussiones Mathematicae
    Graph Theory
    23(2) (2003) 261-272.

  • [35] O. Favaron, S.M. Hedetniemi, S.T. Hedetniemi and D.F. Rall, On k-dependent domination, Discrete Mathematics
    24 (2002) 83-94.

  • [34] S.P. Martin, J.S. Powell and D.F. Rall, On the independence number of the Cartesian product of caterpillars,
    Ars Combinatoria 60 (2001) 73-84.

  • [33] B.L. Hartnell and D.F. Rall, Connected domatic number in planar graphs, Czechoslovak Mathematical Journal
    51(126) (2001) 173-179.

  • [32] S.M. Hedetniemi, S.T. Hedetniemi and D.F. Rall, Acyclic domination, Discrete Mathematics 222 (2000) 151-165.

  • [31] J.E. Dunbar, S.M. Hedetniemi, S.T. Hedetniemi, D.P. Jacobs, J. Knisely, R.C. Laskar and D.F. Rall, Fall colorings
    of graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 33 (2000) 257-273.

  • [30] B.L. Hartnell and D.F. Rall, Lower bounds for dominating Cartesian products, Journal of Combinatorial Mathematics
    and Combinatorial Computing
    31 (1999) 219-226.

  • [29] B.L. Hartnell and D.F. Rall, A bound on the size of a graph with given order and bondage number, Discrete Mathematics
    197-198 (1999) 409-413.

  • [28] L. Markus and D.F. Rall, On seed graphs with two components, Ars Combinatoria 49 (1998) 193-204.

  • [27] J.I. Brown, R.J. Nowakowski and D.F. Rall, The ultimate categorical independence ratio of a graph, SIAM Journal of
    Discrete Mathematics
    9 (1996) 290-300.

  • [26] R.J. Nowakowski and D.F. Rall, Associative graph products and their independence, domination and coloring numbers,
    Discussiones Mathematicae - Graph Theory 16 (1996) 53-79.

  • [25] G. Gunther, B.L. Hartnell and D.F. Rall, Star-factors and k-bounded total domination, Networks 27 (1996) 197-201.

  • [24] B.L. Hartnell and D.F. Rall, Vizing's conjecture and the one-half argument, Discussiones Mathematicae - Graph Theory
    15 (1995) 205-216.

  • [23] B.L. Hartnell and D.F. Rall, A characterization of graphs in which some minimum dominating set covers all the edges,
    Czechoslovak Mathematical Journal 45 (1995) 221-230.

  • [22] B.L. Hartnell and D.F. Rall, Bounds on the bondage number of a graph, Discrete Mathematics 128 (1994) 173-177.

  • [21] D.F. Rall, Induced subgraphs of self-complementary graphs, Bulletin of the Institute of Combinatorics and its
    Applications
    9 (1993) 57-64.

  • [20] G. Gunther, B. Hartnell and D.F. Rall, Graphs whose vertex independence number is unaffected by single edge
    addition or deletion, Discrete Applied Mathematics 46 (1993) 167-172.

  • [19] B.L. Hartnell and D.F. Rall, A characterization of trees in which no edge is essential to the domination number,
    Ars Combinatoria 33 (1992) 65-76.

  • [18] D.F. Rall, Domatically critical and domatically full graphs, Discrete Mathematics 86 (1990) 81-87.

  • [17] M.S. Jacobson, K. Peters and D.F. Rall, On n-irredundance and n-domination, Ars Combinatoria 29B (1990) 151-160.

  • [16] S.J. Dow, P.J. Slater and D.F. Rall, Convex labelings of trees, Journal of Graph Theory 11 (1987) 59-70.

  • [15] C. Peyrat, P.J. Slater and D.F. Rall, On iterated clique graphs with increasing diameters, Journal of Graph Theory
    10 (1986) 167-171.

  • [14] D.F. Rall, A class of rings which are algebraic over the integers, International Journal of Mathematics & Mathematical
    Sciences
    2 (1979) 627-650.

  • Book Chapter

    B.L. Hartnell and D.F. Rall, Domination in Cartesian products: Vizing's conjecture, Domination in Graphs: Advanced Topics,
    Pure and Applied Mathematics Series,Vol. 209, Marcel Dekker, Inc., New York, 1998.

    Conference Proceedings

  • [13] B. Hartnell and D. Rall, A vertex-magic edge labeling game, Congressus Numerantium 161 (2003) 163-167.

  • [12] R. Jamison, S.T. Hedetniemi and D.F. Rall, Equal unions of maximal independent sets in bipartite graphs,
    Congressus Numerantium 141 (1999) 185-190.

  • [11] C.A. Whitehead, B.L. Hartnell and D.F. Rall, The watchman's walk problem: an introduction, Congressus
    Numerantium
    130 (1998) 149-155.

  • [10] B.L. Hartnell and D.F. Rall, On graphs in which every minimal total dominating set is minimum, Congressus
    Numerantium
    123 (1997) 109-117.

  • [9] J.E. Dunbar, L.R. Markus and D.F. Rall, Graphs with two sizes of minimal dominating sets, Congressus Numerantium
    111 (1995) 115-128.

  • [8] G. Gunther, B.L. Hartnell, L.R. Markus and D.F. Rall, Graphs with unique minimum dominating sets, Congressus
    Numerantium
    101 (1994) 55-63.

  • [7] G. Gunther, B.L. Hartnell and D.F. Rall, A restricted domination problem, Congressus Numerantium 94 (1993) 215-222.

  • [6] G. Gunther, B.L. Hartnell and D.F. Rall, On maximizing the average order of surviving components, Congressus
    Numerantium
    92 (1993) 97-104.

  • [5] G. Gunther, B.L. Hartnell and D.F. Rall, Critical beta- stable graphs, Congressus Numerantium 86 (1992) 55-64.

  • [4] B.L. Hartnell and D.F. Rall, On Vizing's conjecture, Congressus Numerantium 82 (1991) 87-96.

  • [3] D.F. Rall, Dominating a graph and its complement, Congressus Numerantium 80 (1991) 89-95.

  • [2] D.F. Rall, A fractional version of domatic number, Congressus Numerantium 74 (1990) 100-106.

  • [1] D.F. Rall and P.J. Slater, On location-domination numbers for certain classes of graphs, Congressus Numerantium 45 (1984) 97-106.