<p>In this paper, we study the homological properties of edge rings of some complete split-like graphs, namely, extended complete split-like graph <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {ECS}^a_b\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mrow> <mi mathvariant="script">ECS</mi> </mrow> <mi>b</mi> <mi>a</mi> </msubsup> </math></EquationSource> </InlineEquation> and multiple complete split-like graph <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {MCS}^{a}_{b,n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mrow> <mi mathvariant="script">MCS</mi> </mrow> <mrow> <mi>b</mi> <mo>,</mo> <mi>n</mi> </mrow> <mi>a</mi> </msubsup> </math></EquationSource> </InlineEquation> encoded in the minimal graded free resolution of edge rings of these graphs. In particular, we derive combinatorial formulae for their graded Betti numbers, Castelnuovo-Mumford regularity and the projective dimension. In addition to this, we also discuss, when such graphs are well-covered, vertex decomposable, shellable, Cohen-Macaulay, sequentially Cohen-Macaulay etc. As a consequence, we also obtain the formulae for graded Betti numbers of various families of graphs, namely, complete split graph <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal{C}\mathcal{S}^a_b\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">C</mi> <msubsup> <mrow> <mi mathvariant="script">S</mi> </mrow> <mi>b</mi> <mi>a</mi> </msubsup> </mrow> </math></EquationSource> </InlineEquation>, windmill graph <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(Wd(b+1,n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mi>d</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, friendship graph <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(F_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>F</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> and star graph <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(S_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> as a special case.</p>